What it means
A mug is an easy mark, someone gullible who’ll believe any old chat and end up paying over the odds. Telling someone don’t be a mug is basically wise up and stop getting played. Different thing, getting mugged is being robbed in the street, not just looking daft. Nobody wants either, but the first one’s avoidable.
Usage examples
"He dropped 150 quid on a dodgy bag outside Stratford and acted gassed. Mandem told him straight, bruv, don’t be a mug."
"Don't be a mug, nobody doubles your money in a week without a catch."
"They saw him coming and sold the old banger to the poor mug for double."
"You paid upfront for trainers off some random Insta page? Brother, you're being a mug."
"I told her don't lend him cash again, he's making you look like a mug."
Where it comes from
This slang sense comes from mug meaning face, a really old English word with roots in 19th century street talk. From there, calling someone a mug shifted into saying they’ve got the look of an easy victim, then more broadly an idiot or sucker who's being taken for a ride.