It easy and sanitary to clean your wheel down and with minimal movement. As you know the going back and forth with water spilling everywhere is what causes slippery floors and its a big chore. There are four basic cleanup steps:
1. collect the big pieces, dispose as you see fit (collect for your reclaiming, donate to the studio, or throw away)
2. dirty clean your wheel and tools using you throwing water (which is yours and it was fresh when you got it so it would be sanitary.
3. dump your water in the sink and rinse your sponge
4. Wipe down your wheel again with a clean sponge.