The woodchuck is an extremely rare creature – it is not normally generated, and usually must be explicitly created by means of a figurine, stone to fleshing a statue, reverse genocide, or polymorph. Otherwise, it serves no special purpose, apart from being a pain to extinctionists. It can swim. The only way you may ever see a woodchuck in your game without intentionally generating one (e.g. using reverse genocide) is if a monster is polymorphed. Additionally, a chameleon or other shapeshifting creature may assume the form of a woodchuck.
The woodchuck's stats appear almost identical to those of the rock mole, which precedes it in the monster list. The only differences, besides the generation frequency and the glyph color, are its diet, ability to swim and tendency to wander. Note that both the woodchuck and the rock mole are tunnelers and as such can chop down trees and tunnel through rock walls.
Its inclusion is a joke, to do with the Oracle and "How much wood would a woodchuck chuck if a woodchuck could chuck wood?". The joke is a reference to the real life Usenet Oracle. The internet has the entire text of Oracularity 576-06.
This means that if you encounter a woodchuck, you are probably
a) on the Oracle Level
b) on a Bones level
c) accidentally playing SLASH'EM
In SLASH'EM, they are marginally more common, as there's often a single woodchuck generated in the Oracle level. On Groundhog Day, the 2nd of February, you can encounter lots of woodchucks on the Oracle level in Slash'Em, with a recurring message of "No more woodchucks!"
The Usenet Oracle requires an answer to this question!
> How much wood could a woodchuck chuck if a woodchuck could
> chuck wood?
"Oh, heck! I'll handle *this* one!" The Oracle spun the terminal
back toward himself, unlocked the ZOT-guard lock, and slid the
glass guard away from the ZOT key. "Ummmm....could you turn around
for a minute? ZOTs are too graphic for the uninitiated. Even *I*
get a little squeamish sometimes..." The neophyte turned around,
and heard the Oracle slam his finger on a computer key, followed
by a loud ZZZZOTTTTT and the smell of ozone.