'Chuck' means toss or throw. You could possibly say: "How much wood could a woodchuck throw if a woodchuck could throw wood". But 'chuck' instead of 'throw' makes it more of a tongue twister. That's just my interpretation.
Chuck actually means to throw, but the sentence is not particularly meaningful. The phrase is a pun and has to be pronounced correctly to achieve the desired effect.
"How much wood would a woodchuck chuck if a woodchuck could chuck wood?
