You can always cut the damaged meat away if there are puncture wounds.Even if you take the dog's saliva/mouth bacteria out of the equation, if you have puncture wounds through skin into flesh you have exposed it to soil bacteria, bird's own skin bacteria, etc.
Hog dogs are trained to grab the ears. Retrievers are trained not to pierce the skin. Terriers and such are trained to kill vermin without intent to eat, generally. In any case, prompt processing is a safe precaution.