Related: How do you clean cheesecloth?
My problem is a bit more complex. I sprout beans in cheesecloth and it's been working okay. The cheesecloth is able to get some of the bean roots off the beans when I harvest the bean sprouts so that I don't have to eat a lot of roots. The drawback: I end up with a piece of cheesecloth full of bean roots. Handwashing it helps remove some but not all the roots. Better ideas?