Its usually used by a higher-ranked person toward a lower-ranked person for punishment. Wouldn't usually be used during PT, you'd tell someone "beat your face" if you caught them red-handed doing something stupid.
Rarely used by officers when dropping a sergeant for push-ups because of its condescending tone, its almost exclusively directed toward lower ranked enlisted when they fuck up.
Soldier: Uh... uh... no excuse sergeant?
Platoon Sergeant: BEAT YOUR FACE