1. To clean or dry some surface by mopping or wiping it. A noun or pronoun can be used between "mop" and "off." Here, take this cloth and mop off the windows so I can see while I'm driving. I mopped my face off with a towel after coming inside from the rain.
2. To mop or wipe something in order to remove it from a surface. A noun or pronoun can be used between "mop" and "off." I kept having to mop fog off my glasses because it was so warm in the room. It's been too long since I mopped off the dust from these shelves.
mop something off
to wipe the liquid off something. Please mop the counter off with paper towels. Mop off the counter.