From Longman Dictionary of Contemporary Englishwipe something ↔ up phrasal verbDHCREMOVEto remove liquid from a surface using a cloth I hastily wiped up the milk I had spilled. → wipe→ See Verb table
Examples from the Corpus
wipe up• She slapped me when I tried to wipe it up, but I swear she winked at me.• Apply it over the boards with a roller, wait a few seconds, then wipe it up with a clean cloth. 