The term woodchuck has nothing to do with chucking wood. It’s an anglicized version of the woodchuck’s Native American name. (wuchak or otchek)
How much wood would a woodchuck chuck if a woodchuck could chuck wood? Since woodchucks can’t chuck wood, we may never know.
These small North American rodents are known by many names: groundhogs, land-beavers, whistle-pigs, and of course, woodchucks. Most of these are intuitive; they somewhat resemble hogs and beavers, and they tend to whistle when alarmed. But what about woodchuck?
It turns out that the title woodchuck is related to neither wood nor chucking. It’s an anglicized term, drawn from many Native American languages, most directly the groundhog’s Aboriginal Algonquian name, wuchak.
In those areas where they’re known as woodchucks, it’s not because they like to chuck wood. Native Americans had several different names for woodchucks: otchek (Cree), otchig (Ojibwa), and wuchak (Algonquian).
English settlers used the more familiar sounds of their own language to come up with a word that sounded like these Native American names. That’s how “woodchuck” came about.
The woodchuck tongue twister was originally written at the start of the 20th century as part of the Woodchuck Song in the musical The Runaways.