Deer primarily eat leaves and buds, but will eat grass in a pinch. You need horses, cows, sheep, or elk to help with the mowing.
"Deer are selective feeders. They are usually browsers, and primarily feed on leaves. They have small, unspecialized stomachs by ruminant standards, and high nutrition requirements. Rather than attempt to digest vast quantities of low-grade, fibrous food as, for example, sheep and cattle do, deer select easily digestible shoots, young leaves, fresh grasses, soft twigs, fruit, fungi, and lichens."