A cat. A snapper trap. A humane trap and relocation over 5 miles away. Poison. Listed in order of both effectiveness and environmental impact.

I don't think a cat would do much about groundhogs... they are too big I would think... A gun works well, also traps (humane or not, your choice, unless the animal is a protected species)

Please don't use poison if you can avoid it. You don't want to kill pets, children and other beneficial wildlife. If you must use it, be extremely careful, and make sure only the intended target can get the poison.
Plus if they die under your shed, you have to get them out somehow, otherwise they wil STINK!