Destroying the Bark
If the food-transporting phloem is severed all the way around the tree (a process called "girdling"), food cannot be carried to the roots and they will eventually die. As the roots die, so does the tree. Periods of rapid growth, usually from March until June in North America, are the best times to do girdle a tree. These spring growth spurts are when tree bark "slips". The phloem and cork layer easily peels free, leaving the cambium and xylem exposed.
Remove as wide a section of bark as you have time for to make an adequate girdle ring. Then scrape (or chop) into the surface of the xylem to remove the cambium. If any cambial material remains, the tree will heal. The best time to girdle is before the trees leaf out. The process of leafing out will deplete energy stores from the roots, which stores cannot be renewed if the phloem conduit has been interrupted.
Avoid the Sprout!
Some trees are prolific sprouters and produce adventitious twigs near an injury. If you don't remove or kill the entire root, you just may have to control these sprouts. Sprouts coming out below the girdle must be removed as they will continue the process of feeding the roots if left to grow. When you are removing these sprouts, it is a good idea to check the girdled strip and remove any bark and cambium that may be trying to bridge the wound.

