I just cleaned my mat (58 x 32") with one of those miracle cloths that is supposed to clean anything without chemicals. I can't soak this one, but after a cutting spree on a bunch of fleece, I wet the cloth with warm water and went for it. Worked great.
I also use these cloths to clean the carpet after fur-ball attacks. Cold water works and doesn't set any stains. (No, I don't sell the crazy things. :) -- just use them.