To give someone a shiny mug, one pile drives or absolutely destroys them. This could be in the form of a hit or a strong backhand to the face. It can be applied to sports as well. If Chad Johnson got hit so hard that his helmet went flying off, he got shivy mugged.
Past tense
"Damn bro you fucking wrecked that dudes shit"
"yeah bro I shivy mugged his ass"
Present Tense
"I swear to God I'm shivy mugging his ass if he doesn't shut his face hole"