late 15c., mappe "bundle of coarse yarn, cloth, etc., fastened to the end of a stick for cleaning or spreading pitch on a ship's decks," perhaps from Walloon (French) mappe "napkin," from Latin mappa "napkin" (see map (n.)). Modern spelling by 1660s. General sense, of such an implement for cleaning floors, windows, etc., is from 1610s. Of smaller utensils of the same sort used for cleaning dishes, etc., by 1869. Of anything having the shape or appearance of a mop (especially hair), by 1847. Grose ["Dictionary of the Vulgar Tongue," 1788] has mopsqueezer "A maid servant, particularly a housemaid."
"rub or wipe with or as with a mop," 1709 (in mop up), from mop (n.). Related: Mopped; mopping.