The woodchuck is an extremely rare creature - it is not generated in the dungeons, and usually must be explicitly created by means of a figurine, stone-to-flesh 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 is if a monster randomly becomes one when polymorphed. Additionally, a chameleon or other polymorphing creature may assume the form of a woodchuck.
Its inclusion is a joke, to do with the Oracle and "How much wood would a woodchuck chuck if a woodchuck could chuck wood?". 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.