Real Dictionary

mop up
phrasal verb: If you mop up a liquid, you clean it with a cloth so that the liquid is absorbed.

mop up in American English
to bring to an end; finish
to clear (ground, trenches, towns, etc.) of scattered or remaining enemy combatants after attacking forces have conquered the area

mop up in British English
to clean with a mop
noun: the act or an instance of mopping up

mop-up in American English
a clearing out or rounding up of scattered remnants of beaten enemy forces in an area
noun: the act, process, or an instance of mopping up; completion of an operation or action

mop-up in British English
noun: an operation to tidy up after a flood, fire, etc