They're all wrong. All those attempts to explain how superman shaves miss the mark.
To discover the true solution you must think of dust. Why? Because dead skin is one source of dust. Superman grows older (he came to earth as a young child, right?) His super skin grows as well, meaning that some cells die naturally and flake off. These dead cells no longer retain any super power.
Superman gets his power from the radiation coming from our yellow sun. Gold kryptonite destroys the ability of Kryptonian cells to process solar energy. Superman's shaving foam contains minute quantities of gold kryptonite allowing a regular steel razor blade to cut his beard and also acts as an exfoliant to give superman a youthful glowing skin.
The idea that superman uses a grinder on his beard is just silly.
Update: Also used for hair cuts and clipping fingernails. Superman is truth, justice and groomed.