And dubbed, trust me. See you Space Cowboy

If you think that this is too gory, you should try Future Diary or something else like that. Cowboy Bebop is very tame on comparison.

I might be mixing up the animes then. Does the first episode have a train and someone's hand gets cut off or something like that?

Nah. I think you are mixing up animes. Like, there's definitely blood in Cowboy Bebop, but the blood is pretty realistic, and it's never overally graphic.

I'll just have to try it out again then!