+1 mineral spirits to clean. Denatured alcohol will work, too.
But you can prevent that buildup in the first place.
Squirt some mineral spirits in there each time you load your tumbler. When your media gets black, change it (or rinse it in water and let it dry in the sun; it works! Black media to clean, in a matter of minutes.) Use less polish. Prerinse your brass in water to get out most of the dirt and loose residue. Stop your tumbler when the brass is done. Don't run it longer (like leave it on overnight, unnecessarily). This loads up the media with brass particles. The black crud is polish loaded with brass particles and powder residue.
If you take the appropriate measures, your media and tumbler can stay clean for many, many more loads. Treat your media right, and it'll work a lot harder for you.
I used to get the same black crud after every 4-5 loads. I'd get one super bling, shiny batch. Then no matter how long I tumbled, the subsequent batches never got that shiny, again; it took a long time just to get clean brass. Now, I just go for clean and bright, but not highly polished. After a load of brass, the bowl practically sparkles. I can use the same batch of media for 10-20 loads before it gets too slow and dirty.
