The simplified answer as it relates to defense is no.
It may kill it, but it won't reliable stop it any time soon, and will only reliably penetrate certain parts of the animal which don't even include the ones likely to be facing you in an attack.
It will not stop a charging grizzly bear that is really committed unless you get lucky.
Most bear charges are bluffs, so if it was only a bluff charge then the unexpected may cause it to end its bluff earlier than it already had planned and go die someplace.
If on the other hand it was a real charge to attack then outside of a lucky shot that immobilizes it damage from a 10mm is unlikely to stop it soon enough.
However most handguns are not enough, and a 10mm with proper loads is enough to reliably penetrate deeply in many soft areas, unlike more common auto calibers. But those holes even in the soft areas won't create the type of wound needed to stop it, just kill it long after the immediate attack has passed which does you little good.
10mm shouldn't be expected to reliably penetrate the head or shoulder, which are targets one has facing them with a charging bear. These take the big revolvers to reliably penetrate, and while they will penetrate these areas even they won't reliably do enough damage to an attacking grizzly bear to stop it immediately, and the 10mm is puny in comparison.
No handgun actually likely to be carried can be expected to kill the bear outright. Many much more powerful rifles don't.
A more accurate scenario even with the appropriate type of handgun is that it is damaged in a way that prevents it from continue to move well, like its shoulder is damage. Or it decides to stop and run away to die. If it is a large one and happens to be one of those with the mindset to keep attacking, they do so much damage in a short time that the handgun wounds won't reliably prevent it from doing what it wants.
Even a .500S&W while it will penetrate fine does not create a wound that will reliably stop it shot center mass at the attacking bear. And aiming at specific places if it is already close in a real charge or chewing on you is difficult. Though a buddy could be in a better position to shoot one off someone else with such a handgun to good effect presented with a side profile.
However such a gun can immobilize them, and will put a hole in whatever part of the bear is shot, making it and a few other big bore revolvers suitable side arms for large grizzly defense, but far from certain.
Do keep in mind though that these animals once covered half of the lower 48 states in large numbers, just 100-200 years ago when the west was explored and settled. They were wiped out from the vast majority of their range with common black powder arms of less power.
Killing is not too hard, as demonstrated by the extermination with whatever black powder gun a settler had available, often not even the more powerful of their time period.
Stopping a large one attacking can be.
Historic is where they were when the settlers came through.
) BiG Bear if you hit shoulder & vitals with several well rapid placed shots...seriously, though?
