From Longman Dictionary of Contemporary Englishmop something/somebody ↔ up phrasal verb1 DHCto remove liquid with a mop, a cloth, or something soft, especially in order to clean a surface SYN wipe up Mop the sauce up with your bread. He mopped up the spilt milk.2 PMAto remove or deal with something which you think is undesirable or dangerous, so that it is no longer a problem The usual solution is to send in infantry to mop up any remaining opposition. The rebellion has been crushed, but mopping-up operations may take several weeks. → mop→ See Verb table
Examples from the Corpus
mop up• The market will have difficulty in mopping this all up.• With the wringer and mop they make up a mopping system.• For every mopping - up operation that gets into the headlines, how many go unreported?• Some one spills the maple syrup, and tries to mop it up with another table's tablecloth.• Serve on squares of bread, or with bread for mopping it up yourself. 