"The chain in those handcuffs is high-tensile steel." (tosses him a hacksaw) "It'd take you ten minutes to hack through it with this. Now, if you're lucky, you could hack through your ankle in five minutes. Go."
A version of the Sadistic Choice when a person is forced to make a terrible choice — they need to remove one of their appendages in order to escape with their life. Sometimes a villain or Nineties Anti-Hero imposes this choice as a punishment, but in other cases, a character is simply trapped.
Many animals will do this to escape traps in real life. Note that even if a person manages this, realistically they will bleed to death (which might be just what the villain has intended) in a few minutes unless they are able to close the wound, so only try this if you have a plan for doing that.
Amputation Stops Spread is similar but to stop poisoning or infection instead of escaping.
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Anime and Manga
In the final episode of Berserk, Guts has to chisel off his own left hand, which is caught in a demon's jaws, with a broken sword in order to save his love Casca, who is in the middle of being raped by Femto, the demon lord that used to be their former captain Griffith. Though he ultimately fails to help her due to being dogpiled by demons mere moments after finally freeing himself, that doesn't make the moment any less Badass. What makes the scene even more badass is that Guts doesn't seem to be grunting in pain: more like in annoyance that any other time in the series, appendages are flying like confetti, but when he needs his arm detached right then and there...
This proves to be rather fortuitous, though. He gains the Arm Cannon after he heals, which has saved his life pretty much every single time he's clashed with dangerous foes. The ironic thing is that it was his left arm that was always the most protected throughout the series up until the Eclipse.
In fourth Slayers novel, and in the corresponding scene in the Slayers: Revolution anime, fleeing villain Zuuma blocks Lina's Flare Lance spell with his remaining arm (having already lost one in the preceding fight) and manages to escape while completely armless. Lina is fairly stunned. Leads to a quick conversation in another novel. Lina discovers Zuuma is back... and has all his arms. Gourry's response? Shit.
Battle Angel Alita does this a lot, although due to Alita being a full conversion cyborg the amputations or dismemberment are less than permanent.
Byakuya is fighting a villain that can control Byakuya's limbs. Zommari first attempts to control Byakuya's left leg. Byakuya doesn't hesitate to sever the tendons and muscles of his own leg to render his limb useless. When Zommari tries to take advantage of the fact Byakuya's now stuck fighting him one-legged, he learns Byakuya's speed is still incredible but manages to take control of Byakuya's left hand and tries to strangle Byakuya with his own hand. Byakuya again doesn't hesitate and immediately severs the tendons and muscles in his left hand as well. Byakuya's then forced to finish the fight one-legged and one-armed.
See also Soifon, who rather than let her body be completely taken by Barragan's power to age her to a skeleton, has her lieutenant cut off her arm. Afterwards, asskicking ensues.
Hachi faces the same situation, but manages to turn things to his advantage by not just cutting off his arm, but teleporting it inside Barragan, causing him to rot under his own power, killing him.
Inverted in Rave Master. Shuda could have allowed Haru to save his life, but opted cut off the hand Haru was holding and fell to his not quite death.
In Tsubasa Reservoir Chronicle Kurogane chooses to cut off his own arm in order to save Fai's life when they were trapped in the collapsing world of Ceres, making most KuroFai fangirls shriek "CANON!" and CLAMP snicker at their own evilness.
Rin from Mnemosyne breaks her own wrists with such nonchalant indifference, it makes you wonder just how many handcuffs she escaped this way in her very, very long life.
Zoro is dead set to escape from a giant birthday cake (long story) by cutting off his feet and then engaging the enemy. Luckily he's only about halfway through by the time the cavalry arrives.
Zoro likes this trope: his go-to solution for problems is "cut a limb off". Luckily when he's handcuffed to Usopp and suggests they do rock paper scissors to decide who cuts off their hand, Usopp is able to squash this idea before he begins. Zoro apparently thinks this is a good idea because he's sure their doctor can reattach the thing just fine.
"Red Leg" Zeff on the other hand was forced to sever his own leg in order to avoid starving to death by eating it (manga) or in order to save a drowning Sanji (anime). Badass either way.
"Chapter 0" shows that Gold Lion Shiki escaped the sea stone shackles in Impel Down by cutting off his own feet, which he replaced with swords.
Similar to Zeff and Shiki, Kyros, who isn't a Devil Fruit user, cut off his leg, which was shackled by a sea stone shackle, to save King Riku from Donquixote Deflamingo. Unfortunately, Sugar transformed him into a toy before Kyros could save the king.
During Orochimaru's initial attack on Konoha, He ends up fighting the Hokage, who as a desperation tactic attempts a technique that will draw both of their souls into a demon's stomach, there to continue fighting forever. While Orochimaru's spiritual arms are in the demon's mouth, he uses his tongue to wield a sword and cut them off, leaving the limbs paralyzed.
The Fourth Raikage attacks Sasuke while he is being protected by extremely hot black flames, and is forced to sacrifice his arm to prevent the rest of his body from being burned up.
Practically the same happens later to Tobi: his arm is infected by The Virus an enemy spreads by touch so he (non-chalantly) snapped his own arm off, then he punt kicks it into his enemy's face. We just found out that Tobi was so nonchalant about losing his arm because he can grow or attach a new one as needed... and, unless it's a translation error, he can switch out his eyes too.
In Baccano! the... helper to the heroes, Claire, forces the villain Ladd into one of these to save his bride, Lua, to preserve his vow that no one will kill her but Ladd himself. Basically, Claire put a noose around Lua's neck while the trio stood on top of a moving train, and attached the other end of the rope to a stationary post not connected to the train, thus forcing Ladd to either abandon his fight with Claire and save her or continue the fight and let his fiance be decapitated. Hardly a choice at all, since Claire had picked up on just how much Ladd's vow to kill Lua himself was worth to him.
Prior to when Fullmetal Alchemist begins, Ed sacrificed his arm to seal Al's soul in a nearby suit of armor during their botched human transmutation attempt.
And even before that (in-series time), Scarbro transmuted his right arm to Scar to keep him from dying.
Later on, Lan Fan cuts off her (at this point already useless) arm to distract King Bradley from following her and Ling. Of course, given the existence of auto-mail, this isn't quite as life-changing as it might be, but it's still an extremely brave choice to make.
In the 2003 anime version, Kimblee transmutes Scar's left arm into a bomb. Rather than wait for it to detonate, Scar destroys the arm completely and takes advantage of Kimblee's shock to kill him. Soon afterward he sacrifices his remaining arm to save Al from suffering the same fate, resulting in a few unintentionally humorous scenes of an armless man running around Lior luring in Ametris soldiers.
In a chapter of Claymore Claire is obliged to make this decision for her fellow renegade Uma when the Nigh Invulnerable Dolf got ahold of the latter's leg.
In Le Chevalier d'Eon, Durand prevents Mr. Whitehead from taking control of him via the Psalms by cutting off his own arm before the effect of the Psalms could spread any farther than that.
In Kaiji, the title character plays a game called E-Card in which he is given the choice of wagering his ear or his eye. He chooses the ear, to which a device is attached that contains a drill bit which moves closer to his eardrum with each hand he loses. The device also sends vital signs to his opponent which tip him off to when Kaiji is planning to play an important card, and once he realizes this, he cuts off his entire ear and continues the game. And immediately after that, he wagers four of his fingers in a lot-drawing game which he loses.
Erza of Fairy Tail was prepared to amputate her arm to stop the poison from a snakebite spreading through her body, but was stopped on the premise that Wendy had healing magic. Unfortunately, she had been kidnapped by the members of Orachion Seiswith the intent of having her resurrect Jellal, so it was a race against time for the rest of the alliance to save Erza's life.
In the manga Torikago Gakyuu, Mikage, after he's kidnapped by Yuikai, is given the choice of having his ears cut off and becoming Yuikai's slave or being pushed out the window of a secret room in the school's clock tower (tied up, no less). He chooses the latter. Fortunately, Yukan arrives just in time to catch him, but Mikage still gets a good deal of discomfort from his decision.
High School D◊D has Azazel cutting off his left arm when Katrea Leviathan ensnared his arm to kill both him and her when she was about to self-destruct. He regrows it later anyway.
In the DCU, Green Arrowgot his arm stuck in a bomb and was offered a choice between losing his arm (meaning he could never use a bow again) or dying. He chose to die. (Don't worry. He got better later.)
Within the continuity of The Dark Knight Returns, he apparently makes the other decision and has learned to pull his bow with his teeth.
In Watchmen, crazy Anti-Hero Rorschach tracks down a kidnapper who had killed a young girl, handcuffs him to a furnace, and sets his house on fire with him inside, leaving him with a saw. He tells the kidnapper not to bother trying to cut through the handcuffs since he wouldn't be able to make it in time, and then he stands outside, watching to see if the guy manages to escape. He doesn't.
They changed this in the movie because they were worried that people would be reminded too much ofSawnote Not Mad Max?. Instead Rorschach simply cleaved his head open, which is the same thing he just did to the man's dog ("Men get arrested. Dogs get put down.")
In an issue of Marvel's The Initiative, trainee superhero Komodo's legs are injected with poison, which will kill her when it reaches her heart. Her teammate Hardball decides that the best way to deal with this under the current dire circumstances is to amputate the legs. Komodo can regenerate, of course, but this still triggers a phobic reaction, as her civilian form lost her legs as well.
Another Marvel example: in an issue of Iron Man: Director of Shield, Tony Stark cuts half of his foot off with a laser in order to remove a power-suppressing anklet so that he can access Extremis and beat the Mandarin.
In The Metabarons series, Aghnar (the second metabaron) has implanted a lot of miniature bombs in his body and set them to go off if he is mortally wounded. When he faces off against a beast impervious to all his attacks, he shoves his arm down its throat and lets it get bitten off. The bombs in his lost arm then makes the creature collapse into a small sphere.
Batman foe the KGBeast cut off his own arm with a fireaxe after Batman snared it in a loop of cable and and was holding him pinned until the police arrived. Since the cable was too tough to cut with an axe...
The Walking Dead Several times. Most notably, the character Dale is bitten, and needs his leg amputated. Also happens earlier in the series with Allan, however, the amputation doesn't save him.
In Bite Me!, the gang faces off against a magical mechanical monstrosity. At this point, cowardly main character Hunter is the most useless member of the group, since while his True Companions Chuck, Andrew, and Haruka have flame-spewing gloves, earthquake boots, and spinning guillotine blades, respectively, he cannot even lift the massive sword he was given (nor does he believe it's sentient, which it is, and it thinks he's a dumbass). After his entire team is slaughtered by this monster, in his first act of heroism and a Crowning Moment Of Awesome, Hunter plunges his hand in the monster's mouth to grab the heart-shaped artifact giving it life. The creature promptly bites his hand off, but thanks to his unexpected distraction both sides lived to fight another day. Naturally, this event kicks off his Taking a Level In Badass.
In a variant, Two-Edge from ElfQuest has his feet trapped in solid stone by the rock-shaper Ekuar, whom he's kidnapped. He somehow gets free, leaving the empty, foot-shaped gaps drenched in his blood, but precisely how much of his feet he'd also left behind isn't clear.
In the comic book backstory for Lieutenant Jean Rasczak from Starship Troopers, the young marine is the only soldier survivor of the first encounter with the bugs. As he hauls ass back into the dropship, one of the Warrior Bugs traps his arm with its mandibles and attempts to pull him back out. He orders the terrified civilian survivor to seal the door — doing so severs his arm but saves his life.
In the Planet Hulk storyline, Miek chops off his own arm to avoid getting pinned down during a fight with another alien monster. Being a giant insect, Miek has arms to spare, but it doesn't grow back.
In Transmetropolitan, Spider decides that chewing his arm off at the shoulder is the obvious means of escape when he wakes up in bed next to Yelena.
In Hitman, Hakan gets bit by a zombie penguin and immediately cuts his hand off to avoid infection. Subverted when he later learns that it wasn't infectious.
Invoked for laughs in De cape et de crocs, where Armand, a fox, waking up in jail, briefly freaks out and attempts to gnaw his leg, "as any self-respecting fox should do".
Films — Animation
In the animated Transformers movie, Starscream's foot gets caught in a closing gate during the Autobot City attack. He blasts his foot to get free (although what we see damaged is his lower shin). He's intact later in the movie — being a robot, and everything.
Films — Live-Action
The probable Trope Codifier and page quote provider: Mad Max. It's particularly cruel because if you watch the movie closely you'll notice that it doesn't matter which choice the cuffed bad guy makes, there isn't time for him to do either. From speech to explosion is about 3 minutes tops. That said, it could be just movie time. Besides, he'd never have gotten help in time before he bled to death. He was probably better off just getting killed quickly in the explosion.
The movie Saw has two people chained to pipes in a Sealed Room in the Middle of Nowhere. The only visible way out is a rusty hacksaw too weak to cut through the chains, but sharp enough to cut through their feet. Gordon cuts off his own foot, and crawls out of the room to get help. He isn't seen for six movies, but revealed to have survived in the last one. Even as Jigsaw's traps get more elaborate in the sequels, they generally come down to "How much pain are you willing to go through to save your life?"
Saw VI opens with two people in cages who are told that they must remove "a pound of flesh" and deposit it on a scale. The first to do so survives. The fat man of the two begins cutting off chunks of his stomach. The skinny girl cuts off her arm... and wins.
In the 2007 film Beowulf, during the fight with the dragon, the title character ends up severing his arm to get himself in a better position to attack.
However, that isn't a very straight example, since he didn't do it for survival, but to kill the dragon as it was threatening people he loved. By the time he severes his arm, it become clear that he has no intention of surviving the fight.
The opening of Scary Movie 4 parodies the Saw example with Shaquille O'Neil and Dr. Phil about to be killed by nerve gas. After being suckered into cutting off his own leg, Phil realizes it's the wrong one and they die anyway.
Done "backwards" in Se7en, where for the Pride murder, the killer cuts off a fashion model's nose and then leaves her locked up with a phone and a bottle of sleeping pills, so she can decide whether to call the police and survive (with a deformed face) or take the pills and kill herself. She kills herself.
The 2013 remake does it rather differently. The demonic abomination flips a jeep onto the Ash expy(Mia), whose hand get pinned under it. With a chainsaw lying just out of reach and the abomination steadily approaching, the trapped hand must be pulled off. There's also a scene where Natalie cuts off her own infected arm to try to keep the demonic corruption from spreading. It doesn't work, possibly because the demon kissed her forcing its blood down her throat.
A particularly complicated example from the Hongkong comic book movie The Storm Riders. Brooding Bad Ass Bujing Yun uses a skill very much like waterbending from Avatar: The Last Airbender , and carries his dead lover to a mausoleum located conveniently in the desert, where the Big Bad, played by Sonny Chiba, lies in wait. With the arid climate crippling his powers Yun is beaten by the Big Bad's earthbending-esque skills, and Yun even gets the bones of his left arm shattered in a Shout-Out to Chiba's Street Fighter movies. What does Yun do? Promptly TEAR OFF HIS LEFT ARM, using the torrent of blood to pull off a bloodbending strike on the Big Bad, and secure his escape. See the whole thing here. Warning: Crowning Moment Of Awesome.
In Evolution, Dr. Block finds himself host to an alien fly that is burrowing into his leg. He refuses to let doctors cut off the leg in question until he learns that it's headed for his testicles. (Ultimately, they pull it out of his rectum instead.)
In the film version of Hannibal, Starling handcuffs both Lecter's wrist and hers to a fridge to prevent him from escaping. Lecter grabs up a cleaver, remarks that this is going to hurt, and hacks through his own wrist, allowing him to evade capture.
In Repo Men, Remy and his multiple-recipient girlfriend must scan the barcodes of their implanted artiforgs to remove themselves from the To-Be-Retrieved list. The scanners won't work through flesh, and both of them have internal artiforgs, so...
In Slugs, Harold cuts off his hand with an axe after he puts it in a glove with a killer slug inside it. Kinda over-the-top, but so is the following explosion from a single gas canister that destroys his whole house.
And in Terminator 2: Judgment Day, the T-800 has his arm trapped and crushed between two gears, and pries it off above the elbow with a metal bar so he can defend John and Sarah Connor from the murderous T-1000.
In Dead Snow, one of the characters gets bitten by a zombie, and, to save himself from zombification, cuts the arm off and cauterizes the wound. Unluckily for him, a zombie pops up with a bite-based Groin Attack shortly thereafter.
The Boondock Saints: The titular heroes, Connor and Murphy MacManus, have been captured by the Mafia and left handcuffed to chairs awaiting torture and execution. When their captors leave the room, Connor breaks Murphy's hand to allow him to slip the cuffs and get the drop on the goons when they return.
127 Hours is based on the true story of mountain climber Aron Ralston. See it in the Real Life section.
In Buried, Paul Conroy is forced to sever his finger on video, or else the terrorists keeping him hostage would kill his wife and son.
In a Gamera film, the heroic turtle finds his arm pinned to a building by one of his foe's spiny tenticles. His response? To blow his own arm off with a fireball, use said fire breath to light his stump on fire, and then plunge this bloody, flaming mess into his foe's chest(!). This is also undoubtedly an Awesome Moment for the big guy.
One mook resorts to this in Phantasm II after his hand is pinned to the wall by one of the Big Bad's flying Sentinel spheres.
In Cabin Fever 2, the hero, having already had his prom ruined by a schoolwide outbreak of necrotizing fasciitis (it's complicated), gets some infected blood on his hand and so, to prevent himself from getting infected, goes to his school's shop classroom and cuts his hand off with a chop saw. It doesn't work.
The Final: The football star and the cheerleader are forced to cut off each other's fingers in a Sadistic Choice and are then left to live with the consequences.
The Prestige It's more a case of Life Or Livelihood Decision, but the decision by Borden to cut off his twin's finger so that they would have matching disfigurements.
Subverted in District 9. An infection has gotten hold of Wikus, the first effects of it showing up in one of his arms. Distraught, he takes an axe with the intent of cutting off the limb, presumably to stop it from spreading any further. It looks like he's going to do it, but he cuts off a thumb first and the pain prevents him from chopping off anything else. Wikus eventually loses his human life, but it's doubtful cutting off the entire arm would have saved him anyway.
Gerry had to cut off the female Israeli soldier Segen's hand since she was bitten by a zombie in World War Z. Her life was saved as a result.
In RoboCop (2014), Murphy shoots off one of his arms when it's pinned under an ED-209 and two more are bearing down on him.
Dune has a form of this in the test through which Reverend Mother Mohiam puts Paul. The Bene Gesserit nerve induction box inflicts an enormous amount of pain on the order of third-degree burns, while the gom jabbar ("High-handed enemy", which she will plunge into his throat if he pulls his hand out) will kill almost instantly.
Mohiam: You've heard of animals chewing off a leg to escape a trap? There's an animal kind of trick. A human would remain in in the trap, endure the pain, feigning death that he might kill the trapper and remove a threat to his kind. Paul: Why are you doing this? Mohiam: To see if you're human.
At the beginning of Swan Song, a colonel trapped in a bunker orders the soldier and civilian boy who are trying to free him to first cut off his hand and then cauterize the flesh with heated instruments he had them prepare first.
Also in The Summer Tree, the immortal Big Bad has freed itself from confinement by losing an arm, but due to the nature of his immortality it cannot heal and just drips blood and ooze continually.
In The Warlord Chronicles, Derfel faces a variant where, due to complicated circumstances that have grown up over the course of decades, his best hope of saving his wife from a Knight Templar sorceress is to cut off his own hand. He goes through with it and manages to save his wife.
Both played straight and subverted in The Clone by Kate Wilhelm and Theodore L. Thomas when the titular synthetic organism gets on two different characters' arms. The first time, it works; they lop off the guy's half-absorbed arm and he survives. The next time, though, the clone adapts and gets into the second guy's body under the skin and eats him from the inside-out, which they only discover after they've already cut the arm off.
In Stephen King's The Stand, the last survivor of a city steps on a rusty nail, and gets gangrene. Because all the doctors are dead (and the hospitals are ransacked), he can't figure out how to treat it. He tries to saw off his foot, but faints from the pain and bleeds to death.
Also appears in the short story "Survivor Type."
And in the short story "The Mangler". The victim has his hand caught by eponymous machine and is slowly pulled in. Another man discovers that machine cannot be turned off, so he lops victim's arm off with a fireaxe.
Stephen King loves this one. In Gerald's Game, a woman is Chained to a Bed in the middle of nowhere when she manages to semi-accidentally kill her husband. A particular version of this trope is how she eventually manages to free herself — she breaks a glass and effectively scalps her hand, pulling the resulting bloody mess through the cuff. Well it is Stephen King.
In The Druid of Shannara by Terry Brooks, Walker Boh's right arm is petrified, and he has to smash it off to prevent the rest of his body from being petrified as well.
Happens twice in the Age of Fire series. First, in Dragon Champion, AuRon tears off most of his tail after the end is bitten by another dragon with lethal venom, to prevent it from killing him. Later, in Dragon Strike, Nilrasha chews off her own wing, pinned under rubble, to escape being killed while trapped.
Not his own limb, but possibly worse: Hawk from Simon Green's Haven novels once had to sever the foot of a (mercifully unconscious) little girl, to free her from the rubble of a collapsed building. Subverted in that, at the book's end, he meets the girl and her mother, and learns that the local wizards have successfully re-attached the child's foot.
In the Ravenloft novel Death Of A Darklord, an elf's lost arm is regenerated by the powers of a young sorceress. Unfortunately, the sorceress has been tapping into dark forces to heal people, and when the bandaged arm is unwrapped, it's become a grotesque wormy tentacle that attacks everyone in sight. The horrified elf immediately begs his companions to cut it off. Possibly a subversion, as the elf may not even have survived the amputation.
In Pyramids from the Discworld novels, Pharoah Pteppic shakes a stonemason's hand in an attempt to be friendly. His ideas of kingship are a little different from those in his country, and is shocked when the man backs away screaming and clutching his arm. It's explained to him that for the man to use his hand would be a blasphemy against the divine pharoah, which is probably punishable by death. The man's hand is amputated by the priests. When Pteppic protests this the high priest tells him that if he hadn't been restrained the man would have done it himself, with his chisel.
Mindstar Rising by Peter F. Hamilton. The main character and his friend mangle each others' hands so that they can slip them through handcuffs; describing the whole sequence of events, in squicky detail, takes several pages. The hero can use his neural implants to minimize the pain, but not his friend.
In a later volume of the Vorkosigan Saga, Miles (brittle-boned from before birth) is chained up by his enemies; he recalls that on one spectacularly unpleasant occasion, he broke the bones in his hand in order to get out of cuffs; unfortunately for him, since that time he has had nearly all of his bones replaced with synthetic ones, even less breakable than normal.
The Sword of Truth features a sorceress named Adie who had to cut off her leg after being attacked by a magic resistant armadillo/leech hybrid. Subverted later, when she gets infected with a magical disease. When she asks a wizard to cut the infected limb off, he explains the disease is already all over her body.
In L. Jagi Lamplighter's Prospero Lost, Miranda recounts how they were driven from Milan by sorceresses — one of whom set serpents on their soldiers. One soldier chopped off his leg trying to free himself from the snake.
In The President's Daughter series by Ellen Emerson White, a kidnapped Meg faces this problem in the book Long Live The Queen when she's handcuffed in the middle of nowhere. She ends up smashing her own hand to bits with a rock in order to escape. Did I mention that she's already had her knee smashed before this as well?
In Max Barry's Machine Man, Dr. Charles Neumann is forced to sever his left arm at the shoulder. It had already been mostly torn off, and it was either that or bleed to death.
In Peer Gynt, an individual chopped off one of his fingers not to be recruited.
Conan the Barbarian attempts a heroic version of this to crawl to the rescue in Red Nails. He is prevented when he realises he dropped his sword when the trap closed on his leg and it is now out of reach.
Stephen Maturin is forced to amputate many limbs in the Aubrey-Maturin books. At the time this was generally the only option for serious limb injuries, especially with the risk of gangrene. Unlike many surgeons though, Stephen did his best to preserve limbs, only amputating as a last resort. Jack Aubrey suffers a serious arm injury during the battle between the USS Constitution and HMS Java, and his arm is only saved due to Stephens skill and patience. Stephen is also forced to apply this trope to himself when he suffers frost bite in his toes whilst crossing the Andes, informing the crew (during dinner) that he "removed the peccant members" with a chisel.
The Greater Good: When a Tyranid spore's tentacle gets hold of Cain's leg, he can't get a clear shot at the tentacle ... but has a very clear shot at his leg. He orders Jurgen to get the medical kit and revs up his chainsword. And then the Reclaimers play Big Damn Heroes and kill the spore just in time.
Grey's Anatomy: After an injury to her leg (from a plane crash) becomes seriously infected, Arizona Robbins asks her wife Callie not to let them cut it off, no matter what. However, when the infection takes a turn for the worse, Callie is forced to go back on her word and makes the call to have it amputated.
One episode begins with finding a dead woman who was missing a hand. They eventually find that she had bitten it off to escape from a psycho's basement.
In "Consumed", it looks like a cannibalistic serial killer chewed through his own wrist in order to escape, leaving his hand handcuffed to the inside of a car. It was actually staged to allow the killer to exaggerate his mystique.
CSI: New York does this too, except they find the hand before they find the body. Turns out the man, who was an ex-con, had been lured to an abandoned church by his old partner in crime, knocked out and chained to the church wall. He died from a mix of blood loss (from biting off his hand), starvation and hypothermia. According to the killer, he was going to let him out eventually and wasn't at all expecting him to bite off his own hand.
In the 3rd season finale of 24, the final canister of the virus ends up being handcuffed to Chase. With only seconds before the timer is set to go off, he gives Jack Bauer permission to chop his hand off with an ax so the canister can be removed and tossed in an airtight refrigerator to keep it from spreading.
Magnificent Bastard Lucas Buck does a copy of the Mad Max situation to a bad guy in the American Gothic episode "The Strong Arm of the Law." Except the man is handcuffed to his brother, and it's his limb he has to cut off.
In Stargate SG-1, RepliCarter attempts to flee through the Stargate, but Teal'c holds her by the arm. Being a robot, it's a simple matter to detach it, though she presumably does not feel any pain. In addition, next time we see her, she has regrown it.
A variant occurs in Stargate Universe, where Eli is forced to stick his arm through the event horizon of the Stargate, risking a potential Portal Cut if it deactivates, in order to keep it open and prevent the ship from jumping to FTL. If he doesn't, the team carrying the mineral needed to fix the oxygen recyclers won't make it back and they will all die of asphyxiation. Luckily, neither the team or his limb are lost.
Played for laughs in a sketch on Kids in the Hall. The sketch revolves around stereotypical French fur trappers who canoe around an office, trapping people and killing them for their suits. When one of the people chews off their own leg to escape a trap:
Francois: Shall we go after him, Jacques? Jacques: Let that one go, Francois. He has spirit. Someday he may be vice president!
Variant in Chuck, when the eponymous hero is Chained to a Bed: he probably wouldn't have been killed, but the bad guys would no doubt have done some very nasty stuff to him. Casey tells him that handcuffs are a cinch to get out of — all you have to do is snap one little bone in your thumb — but Chuck manages to get hold of the key instead. Later in the episode Casey's forced to follow his own advice.
In a round of the dating game on Whose Line Is It Anyway? (US), Wayne Brady's character is a frat boy who has woken up chained to an ugly woman (Colin Mochrie). He attempts to gnaw his arm off to escape, but fails, and is dragged all over the studio by Colin (whose character is an incompetent 1930s gangster).
In the House season 6 finale, the victim of the week gets her leg crushed under a building. To avoid crush syndrome (even though by then, it would have set in...), House and Cuddy decide to hack her leg off using a scalpel and a crude anesthetic. She was very hesitant to let them, and House agreed with her. She dies of a fat embolism on the way to the ER.
In the first season, the zombies arrive at the rooftop where Merle Dixon has been handcuffed and abandoned by the rest of the group, and he escapes by amputating his hand with a hacksaw from the bag of tools that was conveniently dropped next to him.
In season 3 this happens to Hershel, who is bitten on the leg, forcing the group to amputate it in an attempt to save him. It actually works.
In season 2 of Prison Break T-Bag was forced to re-sever his reattached hand to evade recapture by the police after he was left tied to a radiator by Bellick and a colleague, who were after the D.B. Cooper money he had taken.
The inhabitants of an isolated Russian village use amputation to render their citizens and Krycek unsuitable as test subjects for the Syndicate's black oil experiments.
Downplayed in "Leonard Betts". It's Freedom or Finger Decision in this episode. Betts is handcuffed to a car handle and tears off his own thumb in order to escape. His choice is made easier as he knows the finger will grow again due to his accelerated Healing Factor.
On Teen Wolf, Kate Argent shoots Derek in the arm with a wolf's bane bullet which, since he's a werewolf, causes an infection that will kill him if it reaches his heart. He is literally seconds away from forcing Stiles to help him cut off his arm, when Scott arrives with the antidote.
In a Season 3 episode of Nikita, Nikita and Michael are pursing Amanda in a car chase that results in a crash with Michael's arm pinned and the car on fire and about to explode. Unwilling to leave Michael to die, Nikita is forced to cut his hand off to drag him to safety just in time.
Red Dwarf: In order to save Dave's life from the Epideme virus, they get him to agree that they'll amputate his LEFT arm.
Myths & Religion
Norse Mythology: The gods are finding Giant Wolf Fenrir hard to control and thus decide to bind him, claiming to the enormous wolf that it is a game. As a gesture of good faith, the god Tyr puts his hand in the wolf's mouth and when Fenrir realizes he cannot escape, he bites off Tyr's hand. The story definitely shows the god as honorable and brave, given that Odin, Thor, and others certainly didn't volunteer their limbs.
There is a Native Alaskan totem depicting a boy with his hand in the mouth of a monster. It's a giant oyster that caught him while he was fishing. According to the story, he was given a choice between losing the hand (and his chance to be a hunter) and death. He chose death.
Shadowrun's mega-Badass Kid Stealth was given cement overshoes and tossed into Puget Sound by his enemies. An implanted air tank kept him from drowning long enough to tie ligatures around both legs, then blow them off at the knee with plastic explosives. (He got better... legs, that is.)
Deadlands: "Hogleg" Dunstan, the sheriff of Lost Angels, was handcuffed to the bed inside his own jail cell and the office set on fire around him. He escaped by cutting off his right hand.
Shakespeare uses this one in Titus Andronicus, albeit with a twist: the villainous Aaron tells the title character that his sons, condemned to death on false charges, will be spared execution if Titus cuts off his hand. Titus does so (after arguing with his brother and son over who gets to have their hand removed), but Aaron is just screwing with him and his sons are executed anyway. (This leads to the fabulous stage direction Enter Messenger with two heads and a hand.)
Rudy from Wild ARMs cuts off his own arm to free himself from the grappling hook-like thing which the demon Ziekfried has ensnared him with, when he realizes his sword can't cut through the cord. In the remake, wherein he doesn't use a knife, he uses his gun to blow his arm off, instead.
Dead Space: Extraction, just after the final boss, the main character gets impaled to the ground (well, to the hull of the Ishimura), and has to cut his arm off to break free. And it isn't a Cut Scene.
In Metal Gear Solid 4, Raiden gets trapped under rubble during the escape from Shadow Moses Island and has to cut off his own arm to escape. Although by that point, Raiden is a human head and a spine attached to a robotic body, and he has a new arm by the end of the game.
Though really it was more of a choice between Snake's life and his limb at that point.
Zul'jin from Warcraft is revealed in the Zul'Aman cinematic to have cut off his own arm to escape from High Elves who had captured him and had been torturing him (the torture is how he lost his eye). This is an odd case in that Trolls of the series can normally regenerate limbs including arms unless cursed or forsaken by their Loa Gods, but Zul'jin is still missing the parts years after the event, making it unclear as to how much a sacrifice he thought he was making.
General Warfield from StarCraft II was hit in his arm by hydralisk spikes. He returns to base to have that arm cut off — and replaced by an Arm Cannon.
The Dig has a memorable section where Brink's hand becomes stuck in the rock as it shifts while he tries to grab a life crystal in the rock, and the player has to figure out how to set him loose before gangrene or starvation sets in. Solution? Use a jagged-toothed alien jawbone to saw his goddamn hand off.
You have options. Some are far less pretty than others.
The choice is made on behalf of one character in Kara no Shoujo. In order to save Kuchiki Toko the hospital opts for limb removal due to her poor condition. However, by this point, most of the limbs probably wouldn't have worked well anyway.
Prototype has General Randall, head of BLACKWATCH forces, who's left arm is missing. Diving into the Web of Intrigue, you learn that he was part of the initial operation in Hope, Idaho, and got infected with the Redlight virus. He managed to hack off the affected limb before it could spread to the rest of his body.
In Mother 3, when the party first meets Kumatora, her leg is caught in a trap, and she decided to try and cut her leg off to get out of the trap. It's a good thing that your party came along when it did.
At the very start of Episode 2, the protagonist Lee finds a man caught in a bear-trap, with zombies being drawn to his cries for help. You can choose to either leave the man to his fate, or cut his leg off to free him. Subverted, as he ends up dying from blood loss.
The player is presented with this choice again early on in Episode 5. This time, the choice is whether or not to cut off Lee's bitten arm. Again, subverted in that Lee eventually dies no matter what choice is made: he either falls victim to the virus, or dies from shock and blood loss.
In Episode 3 of Season 2, the group meets Reggie, a man who was in this situation before and had his arm cut off quickly enough so that the infection didn't spread. At the end of the episode, Clementine is given the option of doing this to Sarita when she's being attacked by a Walker.
A drunken encounter on Kingdom of Loathing's analogue of Saint Patricks Day can end in a 'coyote moment':
In Girl Genius, Dimo isn't trapped (poisoned instead) but still has to have a friend remove his arm to keep from dying. Then said arm promptly dissolves from the poison. Though note that, Dimo being a Jšger, this isn't so bad for him — he just has to wait to get it fixed.
Biscuit in Goblins gets infected with a flesh-rotting curse after standing on an Eldritch Abomination's severed finger. He cuts the infected leg off with an axe.
Looking for Group. Warlock Richard is bound by a set of enchanted shackles which are drawing their power from him. The group's healer severs his arms in order to deprive the shackles of their power source, rendering them inert. Subverted in that Richard doesn't appear to be able to feel pain, and that Benny's powers make reattaching his arms a simple matter.
In Schlock Mercenary a murder case where an arms dealer's severed hand seemed to have died several minutes after the rest of him turned out to be an instance of this. The vic was actually his clone who had attempted to assassinate him, he got fried but during the fight the original's hand got trapped under a fallen cabinet so he had to cut it off.
Ruby Quest has the one-handed Filbert. He explains that his left hand was exposed to The Corruption, and he had to amputate it in order to remain pure. He is quite thoroughly infected regardless, but remains deeply in denial about it, even when the Body Horror starts setting in.
In Justice League, Aquaman had to cut off his hand to free himself and save his son.
South Park: Although it happens offscreen, at the start of one episode, Cartman is being reprimanded for handcuffing a kid to the school flagpole then telling him he slipped poison into his milk and he would have to saw through his own ankle to get to the antidote. Just because the kid called him fat.
On (presumably) the last episode of El Tigre, Manny tried using his extendable arm to catch Dijango of the Dead, only for him to set the chain on fire, leaving Manny no other option than to cut it off. Good thing he has a spare at home...
Subverted on Futurama, when a hopelessly Slurm-addicted Fry makes a Soft Drink or Limb Decision, and attempts to chew off his own arms so he can fit through a grating in pursuit of the Royal Slurm.
Played for laughs in SpongeBob SquarePants episode "Idiot Box", when SpongeBob and Patrick decided to play Mountain Climbing Adventure! Their constant yelling and laughing triggered an avalanche.
Patrick: SpongeBob! My legs are frozen solid! Youíre going to have to cut them off with a saw! SpongeBob: No Patrick, I can't do that! Patrick: Why not? SpongeBob: Because I already cut off my own arms! Patrick:NOOOOOO!
"How long will it take to saw through the bracelet, Skipper?"
"Bracelet? I was just going to saw off my foot. But you might have something there, Private."
Coyotes are supposed to chew their own leg off if they get caught in a trap. This leads to the expression "coyote moment". Probably irrelevant, it's about dating: "When you wake up with them sleeping on your arm, and would rather chew it off than wake them."
In Tyler Perry's Diary of a Mad Black Woman, Medea is under house arrest and is trying in vain to get the electronic ankle bracelet off, when her brother tells her about coyotes and says, "Want some hotsauce?"
Many lizards have tails that cleanly break away from their bodies when a predator grabs them by it. Often the tail continues to twitch after such self-amputation, as a further distraction for the predator.
Oddly, gerbil tails work the same way—the "tearing off to let them get away" part, that is. Not the twitching part. And it's the skin around the terrified gerbil's tail, not the internal skeletal structure that falls off a couple days later.
Sloughing off the skin of one's tail when it's grabbed or caught on something is a common defense for many long-tailed rodents, not just gerbils. If you see a squirrel with a less-fluffy tail than usual, that's probably what happened to it.
This (along with terrible pain) is why pet rats should never be lifted by their tails.
Truth in Television: Aron Ralston, number six on the Cracked article "7 People Who Cheated Death (Then Kicked It In The Balls)". While mountain climbing, one of his arms got trapped under a fallen boulder... so he cut it off. With a penknife. A dull penknife. It was sharp when he started out, but he first tried to use it as a lever to get the rock off, dulling the blade. He had to snap the bone completely in two before he could start cutting.
Even worse, Aron decided to wait a few days, hopeful that someone would come and rescue him. No one ever came. So he had to cut off his own arm, with a dull penknife, while dying of thirst. And then he had to survive climbing back down the mountain!
Word of God is he waited the exact right amount of time. Any longer, and he would have been too weak to reach help before dying of blood loss. Any earlier, and the search would not have been developed enough to get him medivaced in time once he did find help to save him from bleeding out.
A similar thing happened to a man named Jonathan Metz, whose arm became trapped behind his boiler when he tried to clean behind it. He realized that not only was he going to die if he didn't cut his arm off, so was his pet beagle Portia, who was wandering around upstairs, hungry and confused as to why he he had disappeared. It was the realization that her barking fits were becoming shorter and less frequent, coinciding with his own weakening state, that made him resort to such drastic measure. Much like the Ralston example, his timing was perfect—the arm hand become gangrened enough that it was relatively painless, and police and EMS crews were converging on his house, alerted by friends who were alarmed by his disappearnce.
Real Life: During the Manhattan Project to create the first atomic bomb, it was stated that if you accidentally poked a limb with a plutonium-contaminated tool, the only recourse was swift amputation.
Used in a fictional book when someone does so and they grab a nearby rotary saw and cut off his arm.
Doctor No used this premise to account for No's robotic hands.
There was one instance of a man who caught a ball of cobalt-60 and had his hand amputated. This would not have been necessary as Plutonium nuclides are actually pretty benign, as far as radiation goes. However, this was not known at the time, like most of the properties of plutonium (which was only just available in macroscopic quantities, and only because of the bomb effort itself). The two incidents with the Demon Core only served to further elevate fears about the lethality of the stuff.
The Civil War. In fact, the civil war hospital where a guy gets a shot of whiskey and a block of wood to bite on while they saw off his legs should be a trope of its own.
Any war before WWII, when antibiotic drugs were invented, not only the American Civil War. Before antibiotics, gangrene was almost unpreventable when wounds got infected.
Considering the effect that .75 caliber Civil War era bullets would have on an arm or a leg, you could get shot today in the most advanced hospital available and still lose the affected limb.
Horrifically subverted in Sierra Leone's own civil war, when rebel war criminals would ask their victims, "Short sleeves or long?", then amputate their hands at either the elbow (short) or the wrist (long). Either way, victims' survival depended on whether the bleeding could be stopped, not on what they chose.
Some rebels practiced a straight version of the trope, merely asking "Hand or head".
Crossed with Dark Comedy in the warnings on some large woodchippers — something to the effect of "Do not stick arms or legs into machine — machine can pull you in faster than you can let go of limb."
Occasionally invoked by rescue workers to retrieve victims of auto pileups or collapsed buildings.
This news story about a man who was forced to cut off his own arm when it was caught in a hay baler in order to stop himself being dragged in.
Frostbite occurs when someone's physiology makes a Life or Limb Decision of its own, withdrawing blood flow from the extremities in a desperate attempt to keep the body's core, and the vital organs inside, from freezing. Better to sacrifice digits, earlobes, nose or even whole hands and feet than to lose the brain or viscera.
Bella Swan: "-n-n-nobody really n-n-n-n-needs all ten t-t-t-toes."
Octopuses can regrow arms, so they've been known to leave an arm to get eaten and swim away, or even to eat their own arms in times of extreme starvation.
Pretty much the case if you need to apply a tourniquet for any longer than a short period of time (read: minutes). Applied correctly, the tourniquet will stop bleeding by cutting off circulation to the limb, likely resulting in loss of said limb (or at least part of it) if left in place long enough. For this reason, tourniquets should only be applied in cases where a person's life is in danger from bleeding out of a wound (a literal life-or-limb situation).