Dogs killing deer isn't near as bad today as it once was but it still happens. I can assure anyone who things that a couple dogs, even relatively small ones, can't run down and then drag a deer down are very much mistaken.
Deer can run faster than a dog for a short time. But, if the dog stays after them the dog is almost always going to run the deer down. Then once the deer is exhausted the dog will go for the deer's back legs until it has the deer hamstrung and unable to escape. Most of the cases of dogs running der down and killing them involve two dogs but I have also seen a number of cases where one dog alone drug a deer down.
The worst part is that actually the dogs don't normally kill the deer they just tear the hide off of it, from back to front, while they tear the hindquarters apart, often eating the hindquarters while the deer is still trying to drag its self away. In many cases the dogs never do kill the deer and just rip it apart while it is still alive and until the deer quits fighting, give up, the dogs lose interest and just leave. The deer might live for days until someone finds it and dispatches it or a coyote comes along and finally kills it.
Dogs attacking and tearing up a deer is not a pretty sight. Once dogs have done it once it all too often becomes a common spot for them and doesn't stop until at least one of the dogs is killed.
Back in the late seventies we had some real serious dog problem around this part of the state. People would get a puppy but once it turned into an adult dog they no longer wanted it. They would then take it out to the woods and dump it out to fend for its self instead of putting it down. Consequently we a number of had packs of dogs running around.
During the winters of 1977 and 1978 we had some deep snow conditions with ice on the river. That was before we had more than just a few coyotes so those dogs had nothing to control their numbers and those packs of dogs became a real problem. During the winter they would run the deer out onto the ice and simply run the deer down, attack them and hamstring them out on the river ice. We had dead and dying deer all along the river corridor. It got to the point where we would take the rifles and set up where we could watch stretches of the river, at one or another of the few places we could get access. We shot many dogs on the ice during those couple years as they ran deer out of the woods onto the frozen river. We also expended a lot of ammunition dispatching injured deer the dogs drug down and left alive on the ice during those years.
Of course the river wasn't the only place the dogs were catching deer. Most of our plowed roads also made escape routes for the deer but believe me it doesn't take the dogs long to run a deer down when the deer can't use normal escape routes and is restricted to plowed roads.
I have also shot a few dogs when they had a deer down, I believed they were local dogs and wanted to find the owner and arrest them for their dogs attacking a deer. If the dogs were just chasing a deer I never shot the dogs though I would fire a round or two in front of them to get them off the deer's trail. If I encountered a situation though where a couple dogs had a deer down and there was tracking snow on the ground I did on occasion shoot one dog then track the other dog home so I knew who the owner was and who to cite now that I had the evidence of what they had done.
In many other cases though I didn't need to kill one of the dogs to get them to lead me to their owner. In those cases I didn't kill the dogs, and preferred to just deal with the owners through the legal system.
Killing dogs should be avoided anytime it is possible control the scene without harm to the dog or dogs. But, make no mistake that dogs can be a very serious threat and cause major damage to the deer in a area once they get a taste for the chase and kill.
As for our local area our coyote populations eventually got our once dog problems under control. Even though coyotes will take fawns and even occasionally kill an adult deer, when conditions are right or the deer is injured, I never saw where the coyotes caused anything close to the damage those packs of dogs were doing before the coyote numbers reached what I consider to be a more natural carrying capacity.
Dick Bodenhorn