Violence and death is surprisingly infrequent. In fact, about half of the episodes don't have any violence in them at all. Those that do, usually keep it brief. However, when violence is present, the show doesn't shy away from showing blood or injury detail, but it's still short of being excessive or gory.
The aforementioned colosseum episodes are surprisingly mild, as there's almost no blood and few people die. This is partially due to the fact that the protagonist refuses to kill her opponents.
Violence is not central to the plot and is not present in every episode, but there are still a few instances. Kino occasionally gets into fights which result in some somewhat violent fights. None of them are graphic, but they tend to be intense and show at least some blood. since the series doesn't always contain these fights, they can be pretty surprising when they do appear.
A girl briefly shoots two rabbits for food, some blood is shown.
A girl kills three men, some blood is shown.
A man is stabbed, he is then shown on the ground in a pool of blood.
Two episodes are featured in a colosseum type area, some fights are seen, they are all bloodless up until a woman is shot with very brief blood seen. Later someone shoots a man outside the colosseum, his body is not shown but some blood is seen on the people around him.
Images of corpses are seen briefly in a later episode.