OMG that is awful!! How about just containing the dog safely so it can't chase deer in the first place?E-collar is an "electronic collar" or you could call it a shock collar. There are a couple ways to break your dogs from chasing deer. One way is to drive around until you see a deer run into the woods. Take a dog out of the box and put him near where you saw the deer. If the dog starts to sniff the trail from the deer, correct him with the collar and then let him sniff a rabbit fur or rag with rabbit scent on it.
Another method is to use breaking scents. You can buy (for pretty cheap) small felt tabs that go on the dogs collar. Saturate the tab with deer breaking scent. After a while, the dog will want nothing to do with the scent and will shy away from deer scent. As a last ditch effort (you have tried these methods and dog still runs deer), you can take a small amount of the deer breaking scent and put it in a small syringe. Squirt a tiny bit in the dogs nose. It will be awful for the dog, but it is a last ditch effort to protect the dog. In many places it is illegal to run deer with dogs. Also, deer run differently than rabbits. If your dog is chasing deer, it can easily run out of your range or even run to a highway, etc. If the dog still runs deer after all of that, it is time to find him a new home.