The major part of the psycho weapon-wielding anime girls are predated by Mariko Shinobu from Oniisama e.... In the last part of the series, when the local Alpha Bitch Aya Misaki mocks her due to her parents's extremely messy and public divorce... an already very unstable Marikosnaps so badly that she slashes Aya's arms, clothes and back with a knife that she had somehow smuggled into her school things. These events get Mariko kicked out of the Sorority... and start the "rolling snow ball" that concludes with the dissolution of said Sorority.
The anime expandsquite a bit on this, and it's even creepier and sadder. Mariko's GWPW stint is predated by a whole episode focusing on her issues with her parents: after finding her father Hikawa with the woman that he cheated on her mother Hisako with and running off as a result, Mariko goes home and finds her "weapon of choice" (in this version, a modern boxcutter) among her school things, and she's this close to use it to slit her wrists open but barely decides against it. Then she takes it to school... and the first paragraph happens.
Her name is Fumio Kirisaki, and that's her up at the top of the page. It's not just some random weapon she grabbed, either: she comes from a family of highly-skilled chainsaw users, and has trained with one for most of her life. It's also heavily implied that her grandfather was the chainsaw-wielding sheriff from The Texas Chainsaw Massacre 2.
Higurashi no Naku Koro ni is built off of this trope, to the point where some call it "the Killer-Loli anime". The series features the iconic, Ax-Crazy Ryuugu Rena, a.k.a. "Cleaver Girl". (The weapon, depending on who you ask, is either a cleaver, a hooked machete, or a billhook/cleaver.) The machete is, mostly, used to find cute things. Mostly. The Sonozaki family has an elaborate torture room that is put to good use, while Shion favors her taser. And even Rika wields a large butcher knife at one point. A syringe also makes a few appearances as a weapon, although it's never actually used for ill — it's always either an antidote for the show's slow-acting Hate Plague or a hallucination (except for when one was used to kill Tomitake). Rika's weapon of choice, however, seems to be a mop, as seen in the Atonement chapter. This is even her weapon in Daybreak, a fighting game.
In an infamous scene from a chapter of Azumanga Daioh, Osaka thought she'd wake up Yukari-sensei by banging on a frying pan, but since she was half-asleep herself at the time, she took a knife out of the cupboard instead, with the result that Yukari woke up to see a groggy-eyed, knife-wielding Osaka standing in the bedroom doorway.
Yukari: W-what? Osaka: Oh, you're awake? I screwed up.
Even funnier in the manga, where she just says "That's too bad." (Referring back to the fact that she's always wanted to try the frying-pan thing, but imagine being in Yukari's position and hearing that...)
It's amazing Yukari managed to get any sleep the next night.
Yamato Nadeshiko Shichihenge: Because Sunako resemblesSadako so closely, it's not surprising how creepy Sunako looks with a knife in her hand. Most of the time it's only there to chop fish with... but it looks creepy nonetheless.
Every angel (especially the main character) in Bludgeoning Angel Dokuro-chan wields a dangerous weapon, usually with extremely violent and gory results.
Skuld in Ah! My Goddess tends to build these to threaten Keiichi with, from the ubiquitous "Skuld-Bombs", to the home-built chainsaw, "Texas Murder" (Murder-kun in the original). This being played for comedy, Amusing Injuries are the worst that can happen.
An extremely unusual instance of this trope occurs in Trigun. Milly is generally a very large, quiet, cheerful woman. However, when danger looms, she pulls out a freaking enormous gun from underneath her voluminous cloak.
Considered it's non-lethal, she can cut loose with unfettered blasting without it ever actually being psycho. But the appearance is there, and certainly cowed a saloon-full of leering thugs in her introduction. Her typically genial smile probably came across as Dissonant Serenity to them.
Milly's gun only counts as nonlethal because its mode of damage dealing involves high velocity blunt force trauma powerful enough to leave targets on the floor in terrifying amounts of agony. Also powerful enough to flip a car.
Hibana from Deadman Wonderland and Renji's her giant whip-sword, as well as all the female Deadman.
Though calling that "a knife" seems like an understatement, considering the damn thing is longer than she is tall. (She does actually carry a knife too, one that isn't bigger than her head... or body.)
Hungary likes to wield a frying pan, but only when she's very pissed off.
Gasai Yuno◊ from Mirai Nikki, to go along with her Ax-CrazyYandere tendencies. People who get between her and her Yuki-kun have a tendency to disappear. Well, not disappear exactly, more... Be replaced by a mangled corpse and a puddle of blood.
Ironically, she has so many psycho weapons that she doesn't have an iconic one.
She seems most comfortable with knives, but has also demonstrated extreme skill with axes, handguns, and even, on occasion, a grenade.
Kokoa of Rosario + Vampire Season 2 turns a small bat named Kyou into any weapon she feels like having. On the front of the second volume she is seen carrying some kind of saw-sword or something ◊.
Probably every girl in Kämpfer could quality, but Shizuku (chained daggers), and Akane (single gun) are the most notable.
There's perhaps an unfortunate lack of female Meisters in Soul Eater to wield Psycho Weapons. But we do have Maka Albarn, with her scythe Weapon Soul Eater. Kim's Weapon Jackie does not look too dangerous as a lantern. Until she starts using her as a flamethrower. Or an explosive at close range. The crazed smile on the lantern's side should have been a hint, one thinks. And then there's Patti wielding pistol Liz with potentially deadly enthusiasm.
And then you have Crona, whose gender hasn't been decided on by the creator. His/Her weapon is quite literally psycho. It's fueled by madness (as it is made of Crona's black blood), and can rip out of Crona's back into either a muscular humanoid or draconic form. Both of which are anchored to Crona's spine. Yecht.
Black Lagoon: Hansel and/or Gretel, when the current Hansel wields the axe (Since they switch personas, if one of them is a girl, it'd be this - at the very least, it'd be Cute Boy With Psycho Weapon). Also Sawyer the Cleaner, a cute-looking gothic woman whose weapon of choice is a chainsaw.
Rin Kagamine from Vocaloid owns a giant roadroller that she likes to squish people with.
And Kiku Juon's Signature items are 2 giant cleavers.
Many, if not all, of the Otherworld characters in the Black★Rock Shooter-verse uses one of these as their Weapon of Choice. The list includes Black Gold Saw (King Saw), Dead Master (Dead Scythe), Srength (mechanical gauntlets almost as big as she is)...Even the eponymous character has one in the form of the Rock Cannon (As an added bonus, she has a Katana as well).
Most Pandora in Freezing. Special mention goes to Satellizer's Nova Blood, a giant razor, and Chiffon's Anti-Nova Trial Version, a giant clawed gauntlet.
Both Erika Furudo and Bernkastel wield a giant scythe in Umineko no Naku Koro ni. The only difference is that Erika's is blue while Bernkastel's is black, not to mention Beatrice and the 7 Stakes, and the Siestas' unhealthy obsession of arrowsthatnevermiss.
Two examples crop up in High School Of The Dead, one playing this fairly straight, one subverting the trope hardcore.
Saeko Busujima is known to be a kendo expert and had practice later on in the afternoon that the outbreak occurred, so nobody's really surprised at the fact that she's wielding a bokan at the time. It's not until later we learn that she rather...enjoys being able to wield her full strength and skill without remorse or worry, and becomes very excited when the main hero gives her a proper sword and effectively tells her to have at it.
Saya Takagi gets her first kill while cornered in a supply closet, and the only thing she can crab at is a power drill. The subversion is that, while she doesn't hesitate (since she, y'know, doesn't want to get eaten), she has a complete breakdown over the situation, so the psycho part isn't so much Axe Crazy as it is post traumatic stress disorder.
In Bitter Virgin, Kazuki wields a pair of scissors and on several occasions has attempted to stab Hinako as she sees her stealing Daisuke from her. When Yuzu asks her about said scissors, Kazuki casually replies they are for "protection from perverts".
Quentin Tarantino wrote one of these girls (Gogo Yubari) into Kill Bill. She used a wakizashi on a perverted salaryman with very gory results and battled the Bride with a saw-bladed meteor hammer.
Fans of Takashi Miike's work may remember a little film named Audition. Asami Yamazaki is gentle and soft-spoken - but what she does with razor wire and acupuncture needles in the last twenty minutes will make even the most hardened horror fan cringe. The appearance of a previous boyfriend in a dream sequence shortly before gives some idea of what she will do to prevent her lovers from leaving her.
At the end of Serenity, River uses a sword and axe taken from the Reavers to wipe out every Reaver in a hallway during the battle on Mr. Universe's moon.
The Japanese revenge-porn movie The Machine Girl is built entirely on this trope; Ami, the title character, is an adorable Japanese schoolgirl with a comically oversized machine gun fitted over the stub of her severed left hand. Before the injury, she wielded a kama sickle.
In High Tension, when the protagonist Marie's best friend Alex is abducted by a depraved serial killer, Marie fights psycho with psycho by wielding a butcher knife, a club wrapped in barbed wire, and even a circular saw in her efforts to get her friend back. In fact the saw is an industrial concrete/steel saw, a tool that can be used to cut through reinforced walls. You could probably take on the Terminator with one of those things.
The quiet female protagonist gets this way when she and her grandfather are terrorized in the movie Axe!.
Yamasaki Asami, the psychotic serial killer from author Ryu Murakami's book Audition, on which the Takashi Miike movie above is based, fits this trope to a T. Not only does she paralyze her victims using a syringe injected straight into the skin under the tongue, but she removes a man's foot with a wire saw and would have gotten the other foot too if she hadn't been killed.
Ysabell was standing in the archway, smiling faintly. She held a scythe in one hand, a scythe with a blade of proverbial sharpness. Rincewind tried not to look down at his blue lifeline; a girl holding a scythe shouldn't smile in that unpleasant, knowing and slightly deranged way.
Of course, due to the level of Retcon in the early Discworld books, when we properly meet Ysabell in Mort, just two books later, she's a perfectly normal (normal enough, anyway) girl, albeit a bit spoiled.
Mitsuko Souma in Battle Royale uses a kama (Japanese sickle) as her signature weapon in all three versions of the story.
In the story Dark Red Mind, the fourth wallcutting Kaitlyn Wernher is a slight example of this trope. Upon first glance, she just seems like an exceptionally cheery twenty year old woman. But it's all a mask. Mentally, she's severely crazy, completely insane and totally fucking bonkers. As for her weapon, she doesn't need one. Her superhuman power is cutting. She can fucking split anything she looks at in half.
Live Action TV
Buffy the Vampire Slayer gives viewers Faith and that wicked looking knife. Buffy with an scythe doesn't count, that's saved for Willow when she goes round the bend when magic is gone from the world, takes the scythe to England, has it ready when she goes to visit Angel and he threatens her after a mass demon attack and not knowing who is at the door, and uses it to slice up his son.
And over on Angel, there's Dana wielding a bonesaw.
There's also Fred. This is practically her thing: Crossbows, Ax-apults, flamethrowers.
Um, Buffy and the rocket launcher, anyone? That she aimed at her own ex-boyfriend and his crew.
Arrow gives us China White, who is a white-haired girl played by the not-at-all unattractiveKelly Hu, yet in every appearance carries a knife with her, and in her first appearance, casually kills somebody by slitting his throat.
April Ludgate from Parks and Recreation is seen threatening Ann while brandishing a comically sizable syringe.
In Ruddigore, when Robin, as Sir Ruthven Murgatroyd, has kidnapped Dame Hannah, she draws a small dagger to defend herself with, but what makes him cringe in terror is when seizes a much larger dagger from an armored figure and tosses the smaller one to him.
"Now then, it's one to one, and let the best man win!"
Aversion: Dragon Age: Origins has Leliana, a heroic equivalent who first shows up trying to talk down the bad guys while dressed in the robes of a priestess (I may add that no priestess has been seen so far in the game with any sort of lethal weapon) and jumps in on your side with a long knife when things go south.
Played almost straight in Dragon Age II with Merrill. While only carrying a simple staff of any kind, she is a Blood Mage who works together with demons, which in the world of Thedas is considered the second highest kind of evil abomination, only surpassed by mages that have become permanently possessed by demons.
In Yume Nikki, Madotsuki can use a kitchen knife, which causes some characters to move away from her if equipped, and is only effective against characters are harmless anyway (Uboa can't be stabbed, and the Toriningen take multiple hits, and will almost certainly get you first). She has 24 effects/items that she can use in total, but judging by the Fan Art, the knife is easily the most remembered.
Molly in The Walking Dead fights with an ice axe she calls Hilda. And she's more badass with it than all the other characters combined.
Little Red Riding Hood from Ever After uses a saw (the second little pig's, given to her by the surviving one) as her signature weapon.
Another Red, this time from No Rest for the Wicked, wields a psycho weapon - an Axe, and is one of the more psychologically unstable characters in the series.
Mell Kelly of Narbonic has an alarming tendency to get her hands on such weapons, which, coupled with her nature, makes her one of the scarier (in a funny way) characters of the series.
Oasis from Sluggy Freelance is a very sweet girl until something comes between her and Torg or she spots a Hereti Corp employee. Then the knives come out.
At one point, however, Torg makes her agree not to use violence anymore, so while she'll still attack Hereti-Corp employees when Override B-1 kicks in, she won't arm herself beforehand while she's lucid, resulting in the use of pencils (and notably a laser cannon she's been told is "the biggest Sharpie they make") as Psycho Weapons. It is AWESOME.
Lily from After Lily wields her psycho weapon (a knife) as early as page 4 with very... bloody results.
Kanaya (grimAuxiliatrix) from Homestuck wields a chainsaw. And is perfecty fine with using it to CUT OFF TAVROS' LEGS WHILE HE'S SLEEPING.
Subverted also in that, in a Mythology Gag reference to Problem Sleuth, the chainsaw often turns into a tube of lipstick. And then double subverted when she coolly applies the lipstick, which is still covered in her chainsaw victim's blood.
Elisa strangles Paw with a scarf and pokes him in the crotch (twice!) with his own dart after it accidentally hit one of her stuffed Phantom dolls.
Jade Sinclair (Generator) of the Whateley Universeloves this trope. There's her cabbit... that turns into a Killer Rabbit and once slaughtered around a dozen badguys in one fight. There's her Hello Kitty compact, which flies... and knives pop out of the sides to become a sinning top of doom. There's 'Spinner', which is basically a lawnmower blade spinning at high speed without the lawnmower engine or housing getting in the way. There's the big athame that she turned into a spinning blade. The railroad spikes. The bear trap. There's a reason she's on the page for Crazy Awesome.
In Worm, the supervillain Bonesaw looks like a young girl with carefully styled curly blond hair. She is actually a Tinker, an extremely talented mad scientist whose specialty is altering biological organisms. She takes pleasure in kidnapping people and using them in horrific experiments, remaking them into monsters. Imp might also fit this more directly, as she is described as a pretty teen girl who walks around with knives and fireaxes, and her Perception Filter superpower makes it easy for her to walk right up to people and stab them, which seems to amuse her greatly.
Clare from Titan Maximum wields a serrated BFS made of aggregated diamond nanorods. note Aggregated diamond nanorods are a real substance.