Where Did Mugged Come from?

According to etymonline, it possibly comes from a mid 19th century thief slang word, "mug", meaning "fool" or "sucker" and is first attested in the meaning "to attack and rob (someone)" in 1864. so to be mugged comes from "being a mug" thus deserving to be attacked...

Why do British people say mugged off?

To be a 'mug' or to 'mug somebody off' basically means to take advantage of or to treat someone as an idiot/fool. This is 'street language' widely used across the UK in both youths and adults. Being mugged off is definitely a phrase associated with white working-class cockney types.

What does it mean if someone got mugged?

an assault or threat of violence upon a person, especially with intent to rob.