Sarcastic humor is biting humor; it hurts. The talent-show judge who rolls his eyes at your dancing and says things like "The average border Collie has more talent than you" is a sarcastic person given to sarcastic remarks.
Sarcastic comes from the Greek word sarkazhein, which literally means "tear the flesh." Maybe that's why we also refer to our talent-show judge's remark as "cutting." When someone's being sarcastic, sometimes it's the tone, rather than the words, that let you know, like when our talent-show judge says exaggeratedly, "Great job! I almost confused you for Pavarotti!" (And then adds "Not!" or gives you the thumbs-down.)
