It is definitely possible - and probably worth while every few months. I usually just take off the top burr and dont bother with the bottom one - its just too much hassle.
If you have been using it for a while and have never cleaned it - get ready for the smell. Its a wonder something that smells so good fresh can smell so bad after a few months.
Check out this CoffeeGeek how-to: http://www.coffeegeek.com/guides/cleanrocky