To wash or wipe with or as if with a mop: Mop the hallway now! He mopped her forehead with a towel.; SYN. mop up, mop.

When you completely remove a liquid from a surface by moving a towel or sponge across it with a sweeping motion, you wipe the liquid up. (Wipe up is similar to wipe off; however, you wipe up a liquid, but you wipe off the surface the liquid is on.)