Sarcastic humor mocks or ridicules, usually by saying the opposite of what is actually meant. The talent-show judge who rolls his eyes at your dancing, smirks, and says, "You ought to be on Broadway" is a sarcastic person.
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, facial expression, or body language that let you know — like when our talent-show judge says exaggeratedly, "Great job! I almost confused you for Pavarotti," as he gives you a thumbs-down.