>>13861918mm Mauser will work, but not the milsurp because hunting needs expanding bullets, and military surplus bullets, by international treaty, do not expand. So you have to get 8mm Mauser ammo specifically loaded for hunting purposes, and that’s fairly expensive, but you can get the stuff online.
Second, there are two types of 8mm Mauser ammo, depending on what kind of gun you have. The American made stuff labeled “8mm Mauser” is purposefully underloaded and has a smaller diameter bullet. This is because the 8mm Mauser (actual name 7.92x57) had its specs updated in the early 20th Century. Before that time, the round ran at a lower pressure, and some late 1800s-made rifles are still around that have a weaker action that can’t handle the new pressure spec. There were also a few very old Mausers that had a barrel a few thousandths of an inch narrower than what is now the standard 8mm diameter. Put any new-spec ammo in those old guns, and you will blow it up. American ammo makers are aware of this, so they load for their ammo to be safe in ALL Mausers, even the super-old ones with narrower barrels and weak actions.
But there’s a downside. If your 8mm Mauser was made after 1905 or so, American ammo will perform like complete shit in it. You won’t be able to hit the broad side of a barn, because the bullet is too small for the barrel. This is where the Europeans come in. If you buy hunting ammo from European brands (like RWS, Norma, Sellier & Bellot, etc), they will load for the 8mm Mauser according to the modern European spec, which uses the higher pressures and the larger diameter bullets, giving you the best performance and accuracy out of your rifle.
The way to tell is by looking at the caliber designation.
“8mm Mauser” is American-spec for the older guns
“7.92x57” is European spec for modern guns.