I can answer part of it - chuck means throw. Oh, and I've just found out that a woodchuck is a groundhog.

1) Some people write the name of the woodchuck "wood chuck", but it does not reflect the etymology: Source: http://schmidling.com/woodchk.htm Here the tongue twister according to this writing, : "How much wood would a wood chuck chuck if a wood chuck could chuck wood? — A wood chuck would chuck all the wood that a wood chuck could if a wood chuck could chuck wood" 1) "The groundhog (Marmota monax), also known as the woodchuck or whistlepig, is a rodent" "The etymology of the name woodchuck is unrelated to wood. It stems from an Algonquian name for the animal (possibly Narragansett), wuchak." Here the full tongue twister: "How much wood would a woodchuck chuck if a woodchuck could chuck wood? — A woodchuck would chuck all the wood that a woodchuck could if a woodchuck could chuck wood" Source: http://en.wikipedia.org/wiki/Groundhog 3) In this saying, chuck means "To consume wood in a rapid manner" Source: http://en.wiktionary.org/wiki/chuck Woodchucks do not chuck any wood, they are not beavers. "Their diet consists of grasses, clover, Plantago, garden vegetables, leaves, twigs, apples, berries, and dandelion. They are not as omnivorous as many other sciurids, but will also eat grubs, grasshoppers, bugs, snails and other small animals."

It basically means: How much wood could a groundhog throw if a groundhog could throw wood? and the answer is: A woodchuck could chuck as much as a wood chuck would chuck if a wood chuck could chuck wood OR A groundhog could throw as much as it damn wanted to

It refers to the tossing out of dirt that a groundhog does when he burrows to make a hole. Since most dirt in a woodchuck's natural habitat contains mulch, which is wood, it's reasonable to assume a healthy woodchuck can, indeed, chuck some wood, else he'd never be able to burrow and survive the cold and escape the predators. So, evidenced by the population explosion of the woodchuck, it seems obvious that he can chuck at least as much wood as necessary to create himself a nice, safe, comfy home.