Moles come to mind right off and although their tunneling can uproot plants they do not eat them. Moles primary source of food are earthworms, which is an indication of a healthy soil. Gophers also will tunnel, but you will find entry and exit holes in those tunnels that will not be there if it is moles. Gophers will eat your plants as will voles, Field mice, that will use the tunnels of others. The most effective means of control is a good, tight fence around the garden with some of the buried at least 1 foot deep with a leg, at least 1 foot long pointing outward from the garden, a backwards "L".
There are numerous poisons that have varying degrees of success as well as various repellants that have varying degrees of succes, all of which can be very expensive to purchase.