Thinking further about this...
That groundhog might have been killed by, for lack of a better phrase, a massive punch to the head. Even if the bullet didn't fracture the skull, the temporary cavity caused by the displacement of the moisture-laden tissue might have had the same effect as a very hard punch. If that groundhog's head was accelerated downward rapidly enough, the brain's inertia would have caused it to be slammed against the top of the skull. That could have caused massive brain damage and even caused enough damage to the cranial cavity so that a breach occurred between it and the critter's sinuses... hence the blood in the nostrils. Perhaps his head snapped down hard enough, and fast enough, to bounce back off the ground... which would compound the brain scrambling, and maybe even cause a bloody nose if his nose hit the ground.
In other words, that groundhog might died from the same thing that kills some boxers in the ring.