There is strong evidence that they do not. Wolves feed on a variety of prey - from as large as deer to as small as mice. Before human intervention, there is no evidence that any prey species of wolves was driven to extinction by wolves. In fact, having wolves around was very healthy for deer. Population control by wolves led to a more stable, healthy population. When wolves were eliminated, deer overran their natural habitats and destroyed them, then died of famine, parasites, and disease. This created the dangerous cycling of deer populations we see today, and also increased the number of deer-born diseases that affect humans, such as Lyme disease.