How would you wash a mouse mat with a design on it like the tomb raider or black ops 3 ones without fading colour or destroying it?
I would probably just use a very mild soap (Dawn liquid dish soap is known to be exceptionally mild and safe for many things) and then air dry the mat on a flat surface.
I'd highly recommend you to scrub it with your bare hands. I wouldn't trust any rough texture to come into friction contact with my mousepads. I learnt a huge lesson with my old White Megasoma.