mug (n.1) Look up mug at Dictionary.com
"drinking vessel," 1560s, "bowl, pot, jug," of unknown origin, perhaps from Scandinavian (compare Swedish mugg "mug, jug," Norwegian mugge "pitcher, open can for warm drinks"), or Low German mokke, mukke "mug," also of unknown origin.
mug (n.2) Look up mug at Dictionary.com
"a person's face," 1708, possibly from mug (n.1), on notion of drinking mugs shaped like grotesque faces. Sense of "portrait or photograph in police records (as in mug shot, 1950) had emerged by 1887. Hence, also, "a person" (especially "a criminal"), 1890.
mug (v.1) Look up mug at Dictionary.com
"to beat up," 1818, originally "to strike the face" (in pugilism), from mug (n.2). The general meaning "attack" is first attested 1846, and "attack to rob" is from 1864. Perhaps influenced by thieves' slang mug "dupe, fool, sucker" (1851). Related: Mugged; mugging.
mug (v.2) Look up mug at Dictionary.com
"make exaggerated facial expressions," 1855, originally theatrical slang, from mug (n.2). Related: Mugged; mugging.