Given the information in this question and its accepted answer, it seems clear that the natural healing process of a human being (or of any other creature) can itself be a deadly weapon if supplied with magical acceleration.
If the body is healing an injury, it requires the ability to supply the necessary energy, materials, etc., needed to physically perform the repairs. If you use healing magic to accelerate that process naively (without accounting for these secondary problems), the body will begin to steal from itself in an attempt to keep up. It's probably going to lose that contest, however; step up the healing rate to a thousand times the normal (which is still short of what would be necessary to get near-instant regeneration, incidentally), and it's a safe assumption that the body cannot increase blood flow by a thousand times, meaning that the tissues around the injury will almost instantly be deprived of oxygen and nutrients.
Give that a little time (a few minutes, probably, before you get gangrene or cell death), and the only result of the healing process is that the damage has actually expanded. You've also weakened the opponent in the meanwhile by drawing off a large part of their bodily reserves for this healing. The accelerated healing will then start up for this new damage, and... well, you can see how this will result in a vicious spiral that can only get worse as long as the healing magic is kept up. The exact cause of death may vary, but my bet is on oxygen deprivation to the brain or general suffocation(hypoxia) as the body steals so much oxygen from the bloodstream that it can no longer fuel essential organs or tissues.