In general, the only legal poisons for use on animals are those designed and used to kill rats and mice, according to Professional Wildlife Removal. Rat poison is illegal to use on other animals, including woodchucks or groundhogs.
Trapping woodchucks is the preferred method of removing them, as Professional Wildlife Removal explains. Traps can either be cages that catch the animals live, or lethal traps that kill the animals when they're captured. In addition, woodchucks can be deterred from gardens by sprinkling Epsom salts on fruits and vegetables, as the animals find the taste unpleasant. Because woodchucks build large burrows that sometimes interfere with buildings or decks, many homeowners want them removed.