means A mug is a sturdy cylindrical cup with a handle, used for hot drinks; the word also means a person's face, a gullible victim, or to attack and rob someone.

from The drinking-vessel sense is old and murky, possibly Scandinavian — compare Norwegian and Swedish 'mugg' for a jug or pitcher. The leap to meaning 'face' likely came in the 18th century from drinking mugs molded as grotesque human faces (the so-called Toby jugs and similar), so a face became a 'mug.' From 'face' grew the slang 'mug' for a foolish or easily-deceived person, and the verb 'to mug someone' — originally to strike at the face — which by the 19th century meant to rob with violence. 'Mug shot' and 'mugging' for the camera both trace back to the same facial sense.