Immortality isn't exactly a superpower you can easily prove to the skeptic. Sure, you can say that you're Really 700 Years Old, but who's to say that they'll believe you? And, while you may have that Healing Factor, you need to be injured for that to work. It's not like you can have your arm sliced open on demand just to prove that you-
Wait a sec, you can.
Self Mutilation Demonstration is the favorite method of Immortals for proving to others their powers. The method is simple: grab a sharp object, slash open your arm (or any other body part), and let your Healing Factor kick in and amaze your guest. In other words, you take Good Thing You Can Heal to its logical extreme, deliberately injuring yourself for the sole purpose of proving you have a Healing Factor. Let's hope you also have the superpower not to feel pain.
Sometimes, the empowered individual will ask someone to just Hit Me, Dammit!. This is either a stylistic variant of the same thing, or a character is using to mock Mooks by revealing that this is one thing they have in common with Superman, particularly to justify hitting them back to much greater effect.
Not to be confused with Self Harm.
Compare Macho Masochism, which is more about harming yourself just to demonstrate how tough you are, without the regeneration powers to back it up. Contrast Impostor Exposing Test, which may use a similar action to prove that the character isn't anything special. See also Immortal Life Is Cheap, which can occasionally be used by other characters to nonchalantly display another's immortality by hurting them severely.
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This was a Once an Episode trick for Yuta in Mermaid Saga. It even got so common that his girlfriend eventually started predicting when the "I'm really five hundred years old..." speech was about to occur and started inconspicuously searching for the nearest pointy object to use.
Huey does it frequently too, though he tends to use more violent methods like setting himself on fire or ripping open his jugular. It's a good way of testing the witnessing "specimen"'s mental fortitude.
Greed proves he has the Healing Factor in Fullmetal Alchemist by asking a flunky to smash his head in with a giant, pointy mallet. It almost happens again later, but he waves down the flunky (already readying his hammer) because they don't have that kind of time.
Ciel does this in differing ways between the manga and the visual novel of Tsukihime. In the manga she stabs herself through her eye to the squicking of Akiha, and in the VN she slits her own throat to the amazement of Shiki.
Kira Sakuya from Angel Sanctuary repeatedly injures his arm to prove to his host body's father that he is actually a soul that has taken over his real son's dying body.
Angel Beats! right off the bat in a variety. Otonashi asks Angel(Kanade) to prove him he's dead. She stabs him in the heart. He survives! ....Or not. Now he knows he's dead for sure.
After draining Joseph Joestar's blood, Dio Brando of JoJo's Bizarre Adventure decides it'd be fun to demonstrate to Jotaro just how invincible he now is by casually ramming his finger through his own skull while he taunts him.
A member of Youngblood once cut off his own arm when asked what powers he had.
In an issue of The Sandman, an Indian fakir, seeking an audience with a powerful sultan, impresses the palace guards by severing his own hand at the wrist (a wound which, naturally, doesn't bleed) and then reattaching the hand with no loss of function afterwards. Subverted slightly in that although he's immensely powerful, the fakir isn't immortal: he does possess a fruit which grants immortality to whoever eats it, but he refuses to use the fruit for himself.
There's a vampire comic by the Finnish artist Petri Hiltunen which starts with the vampire holding a pistol while facing his human guest. The human thinks he's going to get shot, but the vampire actually just wanted to prove to his skeptical visitor that he's a vampire - he shoots himself in the head, and the wound disappears in a couple of seconds. To clarify, the man assumes that the vampire is just a crazy person, and is trying to intimidate him with a gun into agreeing that he is what he says he is.
Batman - "Contagion" features a man who thinks he can do this after walking through a plague zone and being unharmed. Turns out being immune to a disease does not translate into being immune from other harm.
Jennifers Body. Jennifer burns her own tongue with a cigarette lighter, and slashes herself in front of Needy when she decides to share her 'secret' with her.
Terminator 2: Judgment Day has John Connor order the T-800 to show Dyson he really is a robot. The T-800 peels off the skin and muscle of his arm, only to look at the exposed endoskeleton dispassionately.
Jeebs: You insensitive prick! Do you have any idea how much that stings?
In the original Highlander film, when Connor MacLeod decides to reveal his secret to the love interest, he clears up any lingering doubts about his immortality by stabbing himself in the chest with a dagger.
In The Medallion, Jackie Chan's character is made immortal by the eponymous artifact, and tries to prove this to his partner by asking said partner to first shoot (the partner refuses, saying there'd be a ton of paperwork if he discharged his weapon) and then stab him. After he refuses to do that, Jackie stabs himself. On seeing he's unharmed, the partner then takes the knife and keeps stabbing him in awe of the regeneration.
Freddy Krueger does this a few times in the A Nightmare on Elm Street series, mostly just to horrify his victims. In the first film, for example, he says "Watch this!" before cutting his own fingers off, causing a strange green liquid to squirt from them. Later, he answer's Nancy's "What are you?" by cutting into his own chest, revealing more green pus and what looks like maggots under his skin. In the second movie, he emphasizes his "You've got the body, I've got the brain" line by peeling back the skin on his own skull. In the sixth, he cuts off his fingers (again) while counting the ways people have tried and failed to put him down for good.
In the first Wishmaster movie the Djinn blows his brains out at the heroine's command, from which he automatically recovers, thereby demonstrating two things: he must do whatever she says, and he is not to be gotten rid of that easily. He does concede that it hurt like hell.
It's not done to show immortality, so it might not count, but in one Animorphs, a recently freed Hork-Bajir is suspected of being controlled by a Yeerk (parasitic alien brain-living slug). His response is to ram his arm blades into his skull and pull his head apart to show his own Yeerk-free brain. Tobias, the narrator of that particular book, points out "it's not like it didn't hurt him, either. I could see the pain on his face." He has a Healing Factor, but it doesn't make it any less awesome.
In Interview With A Vampire Louis remembers when learning about his new attributes, he jammed a dagger in his arm, and before he could pull it out, the body had healed itself around the dagger.
In the Popol Vuh (Maya mythology) the hero twins use this power to defeat the evil Lords of Xibalba. Xbalanque cut Hunahpu apart and offered him as a sacrifice, and Hunapu rose from the dead. The Lords demanded that the Hero Twins try it on them. The twins did half of the trick...
In Tuck Everlasting Tuck, after realizing he's immortal, to test it out he shoots himself through the heart. It passes right through him like water.
In Thief of Time, a yeti invites Lobsang and Lu-Tze to chop off his head in order to demonstrate the yetis' Save Scumming abilities.
The title character of the Mediochre Q Seth Series, while technically not immortal and also susceptible to pain, demonstrates his Healing Factor to some villains * In the first book to prove that they will probably not win in a fight and should just back down. He opts to blow off his own finger and watch it regrow.
In The Danilov Quintet by Jasper Kent, this trope is inverted, when the protagonist sees a vampire's fingers get cut off and they don't grow back. (It turns out vampires can, with willpower, stave off regeneration. At at the time, several years before the events of the book, it wasn't known that he was a vampire.) Played straight when in the second book said vampire cuts of the same two fingers and lets them grow back, in order to jog the protagonist's memory. The protagonist's son, who at the time is unaware of the existence of vampires, is understandably freaked out.
"Oh, Mister Vandemar," [Mr. Croup] said, enjoying the sound of the words, as he enjoyed the sound of all words, "if you cut us, do we not bleed?" Mr. Vandemar pondered this for a moment, in the dark. Then he said, with perfect accuracy, "No."
The ghost kids in the Goosebumps book Ghost Beach do this repeatedly.
Claire, as shown in the picture above, has been known to do this quite a few times. To prove to herself that she really can heal, Claire cuts off her own toe and watches her foot grow a new one to replace it. It was more to test how well she can heal, not that that makes it any less crazy.
Adam, upon finding out about his Healing Factor, starts to mutilate himself just to watch his body heal within seconds.
In Buffy the Vampire Slayer, when the mayor becomes invulnerable in human form, he has a demon-slaying knight slice his head from the top to his neck. The two side reattach almost immediately. He later catches a letter-opener hurled at him by Angel with his palm, leading to this exchange:
Inverted in First Wave, when Foster is captured by people claiming to be government agents who know the truth about the Gua. To prove he is really human, the agent in charge lets Foster stab him in the hand, as aliens have a Healing Factor. The hand doesn't heal, convincing Foster. Later, it is revealed that all this was an elaborate alien ploy. In fact, it was difficult for them to create an arm that wouldn't heal.
In The Gates, a werewolf slices his arm to reassure his succubus girlfriend that she doesn't need to worry about accidentally hurting him.
The Collector: One of the Devil's clients doesn't remember or believe that she made a deal when the deadline approaches, so Morgan convinced her by cutting himself, showing his hellfire-powered healing.
Diana:(astonished) You've successfully manifested a 4400 ability.
Burkhoff: It's getting there. It doesn't always work.
Diana: ...you just stabbed yourself in the hand.
Burkhoff: Yeah. I was a little worried about that.
A variation in Jekyll. During his Establishing Character Moment, an unfortunate teenager is threatening Mr Hyde with a knife, and saying he'll hurt him if he comes any closer. Hyde says "Ya think!?" and slowly stubs out his cigarette on his own palm. This is not to demonstrate healing abilities ( Hyde doesn't yet realise the full extent of his powers), and is simply to show how un-intimidated he is, but it is still a demonstration involving self-mutilation.
Played with in an episode of Smallville where Clark demonstrates his Nigh-Invulnerability by taking a pistol and firing it several times into his hand. He then drops the expended rounds and shows the other guy his sooty but otherwise completely unharmed hand.
The Nameless One in Planescape: Torment does this rather often. You can even do it to convince someone not to commit suicide. Or you can have him break his neck just to scare people. You can also make good money by letting a jaded Sense Freak experience a sensation of consequence-free murder.
And then, later on, you discover that every time you did that during the game and died, you essentially killed an innocent consequence-free. You Bastard.
Albedo from Xenosaga on at least two occasions shows off his immortality through self-decapitation.
A variation of this trope is used in Ever17. In the Jellyfish Gondola, Tsugumi shows that she has a disease that makes her immortal by killing her pet hamster Chami, which is also infected by the disease. After seeing Chami's shocking sudden death, Takeshi sees an even more shocking sight as the hamster just regenerates so quickly that it looks like he never died after only a minute.
Jurinjo of Emergency Exit makes a large cut in his arm to prove his healing powers to Jason so that he can fix Karl's face. He still feels the pain though.
Retroactively occurs in Homestuck. Gamzee, at one point, parries Nepeta's claw attack and decides to scrape it against his face. Later, we learnt that Gamzee is functionally immortal, not because he reached God Tier as was initially believed, but because of literalJoker Immunity.