There are several ways to clean a cheesecloth so do not pitch it after it seems unusable.
Lemon juice is a great cleaner and won't have an effect on the taste on whatever you use it in next. A lot of people think it will, but it doesn't.
When using lemon juice to clean cheesecloth, lay it in the sun after washing it in the lemon juice. You can also wash it with gentle soap, boil it, air dry, and then store it in a plastic bag for the next time you want to use it. It is possible to clean your cheesecloth by throwing it in with your load of white laundry and adding the detergent and bleach but be sure your washer is set on a gentle cycle because cheesecloths can tear.
Oxy is a great cleaner for whites and works well on cleaning a cheesecloth. You may want to use that in place of your detergent or even with it. Don't throw the cheesecloth in the dryer though because you don't want it getting linty. Take it out and air dry it. If you're not as picky about getting stains out of your cheesecloth then you can just rinse the cheesecloth and drape it over something to dry as soon as you use it.
Baking soda is a great material cleaner, especially for whites. Just take a wet toothbrush and rub the baking soda over the cloth. You may need to add a couple drops of water but this is a very effective method. After scrubbing with the toothbrush just simply rinse the baking soda off and the cheesecloth should be stain free. Sometimes an easy way to clean cheesecloth is to just run it under a heavy flow of cold water and then soak in hot water mixed with mild dish soap. Then after soaking for about an hour rinse it back off with cold water and set it out to air dry.
The sprayer at your sink will most likely get any crumbs off your cheesecloth. Regardless of how you clean your cheesecloth it is wise to boil the cheesecloth prior to using it to sterilize it and make sure there are no tastes from the cleaning process. Don't feel like you have to throw your cheesecloth away when it's dirty because it can be cleaned with one of these ways or even possibly a way not mentioned.