Punches, kicks, and swordfights, but all very cartoonish. Sometimes there is blood and "red" cuts.
The opening has a decapitated arm inside a hollow tree. Very fast, can't be seen without pausing.
Finn kills a monster shaped as a heart, red blood sprouts all over. Very brief and the blood have not stained anything.
In a few episodes we see bruises and scratches, but no blood.
Some fights include decapitation of small parts (noses and hands), but no blood, only flesh wounds. Some monsters have discolored blood when killed.
Several fight scenes are played out for humor. For example, there is a character named "Ash", who everyone hates, since he is a douche. Marceline kicks his crotch and Finn starts beating him up with her. Finally Jake stomps him with his giant foot. Even the Ice King (Simon Petrikov) in one episode punches him with no good reason.
Finn and Jake start beating up each other, because they are proving themselves who is more resilient. Both of them have lots of nasty looking bruises, cuts and some blood.
The Magic man turns a bird inside out making it show the birds guts, flesh and everything else. He also turned Finn into a giant foot, used magic to sew some Martians hands together and turned the Martians drinking water into hair (which they drank!).
Visible green vomit in some episodes, when the characters are disgusted. Jake explicitly vomits into a Jacuzzi after hearing how his wish can destroy and kill many people.
A pale skinned, creepy looking woman in a TV eats her own hair. She gags a lot, and is all the time ready to vomit. Jake and Finn are absolutely disgusted. Must be a reference to shock sites!
Finn has a rash on his leg in one episode. Some kind of disgusting pink liquid/puss drips from it.
Skeletons are seen in some episodes also, walking skeleton get smashed. Some character practice necromancy.
In one episode Ice King stole parts of other princesses bodies and made a monster out of them. Princess Bubblegum got half her face torn-off to set an example!
A demon gets half his body torn off by a laser. All his insides show, and a lot of blood.
A demon starts vomiting bananas and another one gets his head turned into abdominal muscles!
When Hunson Abadeer (The lord of evil), appears from The Nightosphere (Hell), he reconstructs himself to the real world in a gory manner. All his organs, blood and skin stick together, and create him in a brief scene!
Castle Lemongrab has rooms filled with guts, a room with a giant heart and a room with a monster that peels it's skin off to reveal it's skull.
The Lich has skin peeling off his ancient, rotten flesh and what seems to be veins hanging from his arms. He looks very disturbing indeed, to the point of vomit inducing.
Finn presumably "kills" the Lich by shoving a sweater inside his (the Lich's) eye socket, and proceeds to pull through the other socket so that the sweater comes out between the sockets. And it does, breaking the Lich's skull.
The episode "The Enchiridion!" the original title card showed Finn in a dark place holding Jake down on a table with a dagger stabbing him, with a lot of blood and Jake's guts being showed in a very gory style and his eye socket completely mutilated, but Cartoon Network found that image too scary. Subsequently, three versions of the title card were made. The final title card had several changes to be less scary.
Goliad squashes an innocent bee.
A demon sucks up almost all of Jake's blood. The blood is shown. A sword is made out of a demon's blood.
The episode "Too Old" depict extremely graphic cannibalism, and on-screen murder.
In the episode titled "The Jiggler" a creature that Finn and Jake take home becomes violently ill and spews what appears to be blood or vomit out of many orifices of its body. In an effort to stop the leakage, Finn and Jake plug up the holes, only to have the creature expand and eventually burst. Jake and Finn are covered in twisted strands of the creature's body as Jake remarks "Our pet exploded".
Several instances of limb removal, mauling throughout the series (i.e. arms chopped off).
Some episodes have relatively hidden assassination and suicide plots.