Buy a couple of rolls of carpet protection film, it should stick to your floors, overlap each section and you'll basically have a very large plastic sheet which most of the water and dust will stay on top of instead of soaking into the floor, you should then be able to mop or wet vac the worst of the mess up before rolling up the remains into a ball when taking the film up.
Handling a 300mm grinder while skating across wet plastic flooring........
..... what could possibly go wrong?