This is a cartoon, but the animators take the extra step of showing many internal organs of the characters (because of their two dimensional nature). Many characters are assassinated / executed by having extremities sliced off, or by having their bodies cut in two. Whenever this happens, all the severed blood vessels (and any other internal vessels) are shown spewing blood.

Later in the story, there are many sequences in which the main characters race through streets filled with the corpses left as they died, cut to pieces and with blood around them.

There is a "purge" in which the King calls a meeting to talk peacefully, but meanwhile he has the hall surrounded by soldiers. At an appointed time, the soldiers march in and slaughter many of the characters, leaving their severed bodies bleeding. This hall is revisited later, still full of the corpses and the pools of blood.

An assassination / execution of a very colorful and comical character takes place, with him still pleading as his extremities are sliced off, one at a time, and finally falls silent in his blood. His death is signaled by his eye turning into an "X" cross.

One character backs out of an alley into the street, during the reign of terror, and is quickly sliced in two by a passing soldier.

During a dream sequence, the Square meets the King of Lineland, who stabs the Square through the eye.

Women in Flatland are straight lines, with an eye on one end and a mouth on the other. A woman is shown committing suicide, to the fright and bewilderment of the man with her, and then of the men who rush up. She kills herself by detaching her mouth, which then turns around and eats her entire body, bite by bite, until the whole body disappears, including the mouth.

War breaks out in Spaceland. We see a mushroom cloud. We see fire balls, and flames, coming straight at the camera as the characters retreat.

The two dimensional Square becomes weak and ill as he is in three dimensional Spaceland. He faints, hallucinates, and possibly dies. The Sphere, on the other hand, definitely is killed.