I can't tell from the picture of the markings on the receiver ring, but if your rifle is marked 8X60S, then it uses the .323" (Spitzer) bullet. Without the "S" mark, it is most likely a .318" bore.

However, to answer your question, you can indeed pull .323" bullets and substitute the .318" ones, but the case neck will likely need to be resized in order to firmly hold the smaller diameter bullets, which would mean neck sizing with an appropriate die.

Once you have the correct sizing die with the correct expander plug, remove the decapping pin. Then pull the bullets from all the ammunition you want to change bullets in, place the cases with the powder still in them in a loading block to hold them upright, and empty the powder from the first case into a small container.

Resize the empty case and replace it in the loading block. Using a powder funnel, pour the powder from the second case into the first case, then repeat the process with the second case, all the way to the last cartridge, into which you pour the powder from the first case.

You now will have resized and refilled all your cartridge cases, and you can seat the proper bullets in them, first checking the cases with a flashlight or other portable light source to make sure the powder level is the same in all of them.

Be sure that the .318" bullets you replace them with weigh no more than the original .323'" bullets.