This is a term derived from the commonly known insult 'mug'; meaning someone who has been treated like an idiot, or been severely nieve.
If you have been 'mugged off' someone has clearly made you into a 'mug', hence you have been insulted deeply. A 'mugging off' often deserves a swift backhand across the perpetrator's derriere.
'If you don't stop dissin me crew you're gonna have the ultimate muggin off in front of your pals'
When someone disrespects you, and causes offence by insulting you, how you act, or your style. sometimes when your posesions are mugged off. Can result in you cutting them first if mugged off infront of ones pals. (being mugged off infront of your pals is 10 times as bad, as it makes you look like a mug)
for reference watch football factory.
"yo bruv, your wheelsaint fly"
"hey jason, you failed at life"
or when your at a party and you get mugged off and then mark wont answer if hes mugging you off
Having someone masturbate you with one hand, then catching the jizz in a mug that they are holding with the other.
"I met an interesting girl/boy last night. Gave me a right good old mugging off."
or
"I was down at Whatever Bar this weekend. The number of people who were looking to get mugged off was surprisingly low" / "Really? There must be a mug shortage in town".
or
"Had a disappointing evening. Got mugged off with a flimsy plastic cup." / "Well, ceramics is a dying art."