None.
From Wikipedia:
The name woodchuck has nothing etymologically to do with wood. It stems from an Algonquian name for the animal (possibly Narragansett), wuchak. The apparent relationship between the two words has led to the common tongue twister, "How much wood would a woodchuck chuck if a woodchuck could chuck wood? — A woodchuck would chuck as much wood as a woodchuck could chuck if a woodchuck could chuck wood."
