mop up with (something)
1. To wash (some surface) by wiping or mopping with some cleaning implement. I hate having to mop up with this dirty old thing. Let's go to the store and buy a new mop! I didn't have any cleaning supplies, so I had to mop up with some water, dish soap, and paper towels.
2. To remove something (from some surface) by wiping or mopping it up with some cleaning implement. Don't mop up the red wine with our good towels—it'll ruin them! Make sure you mop up that goop with bleach to decontaminate the floors.
mop something up with something
to clean or remove something from something else using a mop, rag, towel, etc. I can mop the mess up with this old rag mop. She will mop up the mess with the rag.