I receive a fair number of phone calls and e-mails each month asking about this or that, and each spring I can be certain that most of those calls will deal with one subject groundhogs. A typical call would be "I've got a groundhog digging under my house (barn, outbuilding, etc.) What can I do about it?" Possible answers are always extremely limited.
Woodchucks are simultaneously both the smartest and dumbest animal around. They're super smart and wary because for tens of thousands of years every hand, paw, and claw has been raised against them. They've been killed and eaten by cougars, wolves, coyotes, bears, and every Indian kid old enough to hold a bow. It's been survival of the fittest, and the unfit have died en masse, leaving survivors whose caution is practically bred into their genes.
The dumb part comes when a young chuck is forced to go walk-about and look for a new home. If he decides to dig under your garage, nothing will stop him. When he gets a location locked in his little pea brain, he's going to dig there. Or else. People have tried everything to send them away. Stink bombs, moth balls down the holes, you name it. They come back. Traps almost never work. I've tried big Hav-A-Hart live traps baited with everything you can imagine, and even covered with grass and straw. Never caught one yet.
An old farmer told me that he got rid of his woodchuck problem by purchasing something at a grain elevator or equity that could be put down the hole, then each of their several exits covered and the animals gassed. That might be something to look into. But the one method that really works, at least if you live in the country, is to shoot them. That gets results every time. But even this can be difficult to do.