Answer: If the rabbits (or whatever) have eaten a substantial amount of bark, or if the tree is completely girdled, then the tree most likely will not survive. If it is a rabbit or other critter, you might try making a ring of heavy duty wire mesh around the tree and/or using a repellent spray made for rabiits. Since it is a dogwood tree, however, you might look carefully for evidence of earlier borer damage as well, since this is a typical symptom of that.
Finally, it could also be due to careless use of a string trimmer. This is a very common cause of death in young trees. Instead of growing grass right up to the trunk, create a ring of mulch around the tree --that way, you can mow right up to the mulch. This saves labor, reduces the risk of injury to the tree, and will also help the tree by reducing competition for nutrients and water from the grass.
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