A deer stomping a dog is a very rare thing. The only reason these mild mannered animals would hurt another animal is defending its young fawns or itself. In this video, the deer is protecting its fawn from a dog that is in the wrong place at the wrong time.
A curious cat is also warned away by the mother deer. If you find a fawn, and the mother is around, this could easily happen to you, so leave a fawn alone if you find one.