Irony employed in the service of mocking or attacking someone is sarcasm. Saying "Oh, you're soooo clever!" with sarcasm means the target is really just a dunderhead.
Sarcasm is sometimes used as merely a synonym of irony, but the word has a more specific sense: irony that's meant to mock or convey contempt. This meaning is found in its etymology. In Greek, sarkazein meant "to tear flesh; to wound." When you use sarcasm, you really tear into them. A clever person coined the variant spelling sarchasm (a blend of sarcasm and chasm) and defined it as "the gap between the author of sarcastic wit and the person who doesn't get it."