Things often get vicious in the animal world. It's always survival of the fittest. When it comes down to a deer verses a dog,  most times the dog will win. Deer can run very fast but only for very short distances and then they have to rest. Most large dogs have much more stamina than a deer. I have seen many instances where a dog will get the best of a deer. But it doesn't always work like that. Check out this video of a Boxer and a deer.