The entire series is about a group of teens trapped in a high school, they only way they can leave is if they kill each other. Once a person is murdered, an investigation takes place and eventually a trial. If the wrong person is sentenced as the murderer, everyone will be executed while the real murderer is allowed to leave. However is the correct murderer is sentenced, they will be properly executed. This is the basis for the entire series.
Many characters are executed in the show, as graphic as that sounds, all of the executions are bizarre and designed like a deathtrap akin to something from "Looney Tunes". The characters do die though and although it's presented with dark humor from Monokuma (the judge/executioner/principle), the deaths are mourned and taken very seriously by other characters.
Lots of blood from the murder scenes and some executions, although it's shown as a hot-pink color and there is no gore. The series has a lot of dark humor involving death or pain.
A man is blasted off in a rocket ship, when the rocket lands and opens, it reveals the man's skeleton (albeit a very cartoonish one).