Deer lack upper incisors and they leave a ragged edge on the branch. Excluding rabbits from the garden is the best way to deal with them. Bury the fence 1 foot in the ground, leaving 2 feet above ground. Individual plants and trees can be protected with wire mesh cylinders. Repellents may provide some short-term control.
Trapping is possible, but check with local wildlife authorities first.
Dogs and cats. Nothing is more frustrating than to have a dog run through your newly planted garden or to have a cat use it as a giant litter box. Here again, fences are a good idea. If your dog is the culprit, training is the key. Odor repellents may help temporarily.