Getting rad has its price, especially on a MTB and one of the ways to learn you and your bikes limitations is to fall. Here in Texas, that usually means sharp limestone, or brittle, dry mesquite trees are waiting for you on the ground.
One pointer I always try to keep in mind is to always ride with a clean bottle. That just means, no hydration mix or juice. Having a bottle with mix and a bottle with just plain water gives you a means to wash a fresh wound out immediately, rather than waiting to get back to the car or your home.
Wash the wound throughly. Remove any rocks, sand, debris and let it dry. Cover it if you can or just let the air dry it out. Sometimes, even putting sunblock on a fresh wound will sterilize it even more – assuming there’s alcohol in it. Otherwise, carry a small first aid kit in your pack.