Mugs so far only have appeared in the last levels in the Dark Castle Series, which are Black Knight 3 and Black Knight's Showdown & The Final Battle. They are not Enemies, but more Obstacles. They are thrown by the Black Knight, and depending of the Difficulty, will bounce.
The best strategy is to move quickly, the Mugs will only move in a straight line, and are on pre set courses, so there a multiple "safe spots". Try to use the Shield to avoid getting killed be them.