Recently we discovered an excellent natural remedy that we have used in our home a few times and it really works. Mix half-and-half comfrey powder and cayenne, then add enough honey to make it a sticky goo, then place on the cut or bruise. The comfrey helps the skin heal, the cayenne will stop the bleeding, or help with blood circulation for bruises, and the honey, especially if it's raw honey, will act as a disinfectant.
We used this when my husband bruised his leg up doing Kung Fu. We put the mixture on a large bandage and covered the worst part of the wound. The next day, it was almost comical how the part that was covered with the remedy was almost completely healed and the rest of the bruise had gotten worse.
We also used it on my son's cut, and the bleeding stopped almost immediately. I tested the cayenne on my own wound to verify that it wouldn't sting, and it didn't, so I felt comfortable using it on him. Now when he wants to be "Dr. Peter", he tells me that he wants comfrey and cayenne to heal people.