Groundhog Day aside, groundhogs are actually interesting creatures (I hear that they make a great stew, but I have yet to put that to the test). That being said, they can be nuisances in the garden, but there are non-lethal ways to control them.
Sure, it might not be available at your local hardware store. And, it is definitely used for live training. But, if you simply have to get rid of damaging moles, the Rodenator might be the tool for you.
Besides burrowing large dens in your yard, groundhogs/woodchucks (members of the squirrel family) are also notorious for consuming tasty greens from your garden and flower beds. Sure, you could use commercial poisons and deadly traps…But is it really worth that much trouble?