"Crude" is a word often paired with joke. "I just don't appreciate that kind of crude humor."
You could also use a word referring to exactly what you don't like about the joke: disgusting, racist, etc.
You might like to read these Wikipedia articles on gallows humor and black comedy. In the US, political correctness is beginning to demand that the latter be called "dark comedy." I thought this was ridiculous until I worked for a local community theater. After our ad for "The Pillowman" appeared, someone called wanting to know if it was about African-Americans.