To "minesweep" is to wander through a location where people are drinking, such as a bar or a party, and drink the partially-finished beverages that people abandoned.
I'm low on money this week, but I still want to get drunk, so lets go minesweep that crowded college bar.
To go through a porno mag and cut out or cover up some or all of the landmines.
"Check this shit out. Don't worry, I minesweapt it.