I'm pretty sure they are machine washable, but good ol' hot soapy water will do the trick.
IMHO, those snakes are only good for BP rifles. A buddy of mine uses them on all his guns and convinced me to buy one; after pulling the bore snake through my 308 barrel twice (nice and slow), I ran a patch down the bore- it looked just as black as if I hadn't used the snake. (Yes, I had cleaned on the snake)