1. To lose moisture. In this usage, a noun or pronoun can be used between "dry" and "up." Hey, if you don't want that marker to dry up, put the cap back on it!
2. To remove wetness from something. In this usage, a noun or pronoun can be used between "dry" and "up." Let me get you a towel so you can dry up that spill.
3. To heal an inflammatory skin condition, such as acne or a rash. A noun or pronoun can be used between "dry" and "up." Don't worry, the doctor prescribed something that should dry this rash up straight away. That cream dried up my acne practically overnight.
4. Of an inflammatory skin condition, to become healed or relieved. If the rash doesn't dry up in a few weeks, you should see a dermatologist.
5. To go away or leave. Oh, dry up and give me some peace and quiet!
6. To stop talking; to be quiet. Typically used as an imperative. Oh, dry up already! I'm sick of hearing you complain.
exclam. Shut up!; Go away and don’t bother me! Aw, dry up! I’ve heard enough.
See also: dry