Firing a .311 bullet through a .308 barrel won't hurt anything, as long as the chamber neck diameter is large enough to expand and release the bullet easily. It will be moving when it encounters the rifling and at the low end of the pressure curve. Once it has traveled the length of the bullet's shank in the .308 barrel, the bullet will be .308 also. Of course this assumes a "cup and core" bullet; monolithic bullets sometimes cause pressure spikes in barrels with groove diameter the same as bullet diameter, if there are no relief grooves.
Mike
