Having had to put down numerous deer (struck and injured by traffic) with 9mm over the course of my career as well as observing several deer being put down by neighboring Police Departments who issued/used both .45 ACP and .40 S&W has demonstrated that while these service calibers from 4" to 5" barreled duty weapons are quite capable of putting the animals (deer) down, they are lacking in the ability to do so very quickly and efficiently. Our Departmental policy specifies the use of "headshots" on these animals and I am an excellent marksman and never missed the "mark" in these humane actions.
In most of the situations that I have either been the one dispatching the animals or been present when one was dispatched in such a manner, the animal (deer) usually required more than one shot and sometimes as many as four, before it finally died. This was the norm regardless of the caliber employed for the task (9mm,.40 or .45). Considering that the animal had, in all cases been injured seriously enough by the vehicular impact to be incapacitated (and immobilized) to warrant such action with the attendant damage from such a accident is testimony to how tough they are and that when possible a shotgun (using slugs of course) or centerfire rifle should be used in preference to any handgun round.
I also hunt quite a bit (besides Deer and Elk, I have also hunted Black Bear extensively in the U.S. and been on Safari in Tanzania for Cape Buffalo) and while I am reasonably certain that I could kill a deer out to about 35 yards with my 9mm, I, out of respect for the animal, use a centerfire rifle (.30-06) for the task because it is the correct 'tool' for the task. Were I to use a 9mm for the task of deer hunting, I would be quite concerned that the ensuing tracking job that would most likely follow would probably be a very, very lengthy one if the deer were recovered at all.
I agree with those above (phoglund, ftierson, Charles S, hokkmike, Wineoceros and Mac45 and anyone else that thinks that it is a less than adequate cartridge for the job) who do not believe it to be either an ethical or effective selection for hunting any big game species and implore those considering such a questionable "stunt" to please refrain from doing so and give the respect these beautiful and noble creatures are due and use the appropriate caliber for the job. They deserve it.