I once watched my dog (a Malamute) track a mole as it ran underground; when the critter came to the surface hole, he lunged faster than you could see and came up with the mole. Which he promptly munched down. Sigh.
We have had some success in convincing the burrowing critters to relocate using those sonic repellers; the battery powered ones work best, but they're getting hard to find. But those are only useful in discouraging them from a small area. I stuck one in a newly prepared bed and they left it alone, and when I found a mound by one of my peonies, I stuck one there and the plant is doing fine. They're still out there in the fields, tho, and on the neighbors' properties. It's an ongoing battle.