@CrownAxe is incorrect. This is something I recently started doing with my new love for KMC Mat sleeves and like you, I don't want to spend 12 bucks for new sleeves. What I do is take some war, soapy water and either a rag or paper towel and I rum down the sleeve (both sides) until the black grime comes off of them. I don't rub the sleeve the same way I clean something else or I risk damaging the sleeve and having to replace it since its marked. I just take a finger and press and slide. You'll get a feel for it.
Don't completely wet the sleeve but make sure the rag or whatever you use is at least damp though so you can easily slide across the sleeve. I've done this now two times on the same sleeves. I can say be prepared to set aside two hours to do this since that's about as long as it takes me to clean mine.