One of the nastier ways to kill a character that tends to show up in a lot of Slasher Movies. Quite simply, the killer takes a knife or other blade (or if the killer is a monster, its claws will do quite nicely) and slashes the victim's belly open (often from groin to sternum), usually resulting in the poor unfortunate's insides spilling out.
If the gutting is self-inflicted and a matter of honor, see Seppuku.
Related to Half the Man He Used to Be. If the victim is pregnant, a Traumatic C-Section may occur.
While gutting does not necessarily lead to death, the good majority of the examples are deadly, so Beware The Spoilers!
Since Gaiden is actually a prequel to the main series, Tenpou's death is a deliberate mirror to the backstory of Hakkai, his next incarnation: after he slaughtered a castle full of youkai to rescue his lover, a survivor of the massacre gave him a very similar wound. Once again he winds up crawling with his entrails on display, but this one he survives, thanks to Gojyo dragging him home and getting him put back together.
One Nick Fury miniseries concludes in a two-sided No-Holds-Barred Beatdown between him and an ex-Soviet colonel and culminated in Nick slashing his opponent's abdomen open and strangling him with his own guts.
Minor slasher villain Speed Freek tries this on The Incredible Hulk once. The Hulk has no problem holding his guts in, but then his skin heals over his hand...
Scream provides the trope name (where the killer threatens to gut Casey like a fish if she hangs up on him again) and two examples right in the opening scene, which has both Casey and her boyfriend Steve being murdered this way, with Casey's body being hung from a tree for extra nasty points.
It happens again quite explicitly with Olivia in Scream 4. A deleted scene shows that Jenny and Marnie suffered the same fate.
Near the beginning of Jurassic Park, Dr. Grant gives an impromptu lecture about the possible links in ancestry between the velociraptor and birds while at an archeological dig site. He gets interrupted by an obnoxious kid, who quips the raptor, "looks like a big turkey." So Grant, much to the amusement of his students, teaches the boy a lesson in respect by explaining exactly how that "turkey" hunted and killed its prey. Grant shows him the raptor's middle toe claw and swipes it across the boy's belly then down his midsection to illustrate the cutting motion it used to spill the victim's intestines; finishing his tutorial by telling him that, "The point is, you are alive when it starts to eat you."
Hannibal from Hannibal cuts a man open then throws him out a window with a noose around his neck. His intestines fall out and splatter on the ground. A little earlier in the movie, Hannibal had described how this same method of execution was used on the person's ancestor.
One-Eye executes a man like this in Valhalla Rising. He slices him open, pulls his innards out with his bare hands and throws them to the floor at the man's feet as he dies.
In Jurassic Park, Dennis Nedry dies in this fashion when he has the misfortune of encountering a Dilophosaurus, nicknamed a "spitter" among fans of the films. It blinds him by spitting into his eyes, then rips open his midsection, similar to the way Grant described in the film version. Likewise, Nedry was alive when it began to eat him. His final thought was to pray for a quick end.
In the second book of the Sword of Truth series, Zedd heals a woman who "held her guts from spilling out of a ripping wound in her abdomen."
Many Stephen King books contain this. He especially likes to have characters step on a loop of their own intestines.
An off-screen, er, off-page example is described in the first act of Macbeth; the titular character is said to have confronted MacDonwald and in the end, "he unseam'd him from the nave to the chops / And fix'd his head upon our battlements." How lovely.
In Seeking Who He May Devour, by Fred Vargas, it is mentioned that according to the lore, werewolves are hairless when in human form because all their hairs are inside their bodies ; cutting them open "from the throat to the balls" to check for hairs is the best way to identify them. When Massart, the asocial, hairless butcher is suspected of actually being the werewolf that killed dozens of sheep and Suzanne, it seems that Soliman and the Veilleux really want to do that to him.
A Dry, Quiet War by Tony Daniel involves soldiers from a war at the end of time 15 billion years in the future, who are almost unkillable because their bodies extend into alternate timelines. The only way to do so is to pin down their bodies and inflict great pain on them, so they can't withdraw into other dimensions. After a deserter from the war rapes a friend of the protagonist, he does this by pulling out a soldier's intestine and tying them to a porch, breaking every bone in his body, then killing him in every alternate timeline.
In The Borgias episode "The Choice", Cesare takes brutal vengeance upon Giovanni Sforza for proving very ungallant toward his sister Lucrezia, who has had her marriage to Sforza annulled because of this and other jerkassery, by means of this trope.
One of the possible critical hits you can inflict in Warhammer Fantasy Roleplay — also an easy way to kill yourself when fighting a troll (they are the local staple of Extreme Omnivore with metabolism to match, so gutting one will get you covered in Hollywood Acid with nasty results).
A rejected scene in a Ren and Stimpy cartoon where they're door-to-door salesmen has them knock on a door, and the homeowner angrily grabs them, throws them in the kitchen sink, and guts them like fish. Ren comments "This is gonna be a tough sell, man!"
This is one of the components of Hanging, Drawing and Quartering, probably the single most cruel punishment ever given out for treason (namely the "Drawing" part, which has nothing to do with art whatsoever.)