Around here, there are so many groundhogs, that if you trap or shoot one, another will just move into its territory. I've worked out a shaky truce with mine--I fence the things they really like, and try to keep them out of the rest of the garden with bribery. I leave offerings--half a head of lettuce that's been too long in the fridge, apples past their prime--at the edge of the compost pile, which is in-between the burrow and the garden. I also spot her grazing in the lawn--I don't use pesticides, and have a variety of wild things growing in with the grass.
And once the apples ripen in the autumn, and start dropping, she gorges on them and leaves the garden alone.
Cheers, Sue