Ok, deer are normally killed with a *bullet* - not shot. A single projectile passing into the vitals. At least half the time the bullet passes through the other side. When it doesn't the bullet is either lodged under the skin or is in the chest cavity. The meat in the general area is often discarded anyways due to ballistic shock (ie, it turns to a bloody mush).
Bottom line, contact between the deer and the bullet is brief (often fractions of a second) and localized.
My understanding is that your point underscores the exact reason that some organizations are pushing to eliminate hunting with lead.. namely, animal meat with lead in it is discarded, scavenged upon, and winds up poisoning wildlife. Its particularly troubling when its a species that's already endangered, like condors: