We just cut the top of the skull out of my buck, and the base of the antlers are real gnarly and rugged, and there's a whole bunch of dirt and grass stains inside them, is it safe to boil the base of the rack and the top of the skull?

Are you making a Euro mount? If so, just put the whole skull in a bucket of water with everything under water. Put the bucket outside for a week, drain and use a spray nossle to remove loose stuff, and repeat. Then I'd use a cleaning brush of some sort to clean the dirt/etc. out of the antlers.

If your married I would check with your wife first to find out if it's alright to stink the house up with deer brain soup!!!

Trust me the freakin' candle queen will come alive if not...

Light rumbling boil, not to aggressive, then do some more scraping and boil again as needed.

To me if the dirt and grass was there when you shot it, it just builds character, I personally would leave it there. I like the natural look.