Shopkeepers, residents and workers in the area this morning said they were shocked by the vandalism to the 10-year-old mural, which shows a Teddy bear aiming a Molotov cocktail at riot police.
An organisation called Appropriate Media, an anti-graffiti group, has claimed responsibility for the vandalism and has called for the 'appropriate and legitimate use of public and private property'.
Chris Chalkley, chairman of community group People's Republic of Stokes Croft, climbed up a ladder and began cleaning the emulsion paint off the mural this morning.
He believes the vandals struck late last night or in the early hours of today.
Mr Chalkley said it was the second time the art had been targeted inside two weeks and believes vandals are distracting from the good work being done to improve the neglected area.
He said: "We've done a lot to change the vibe of the area with street art and this is an important piece.
"I think it was voted the second most identifiable image in Bristol and it's an iconic piece of work. People walking past have been stopping and are genuinely quite shocked by what's happened."
Joel Black, 26, from Southville, who works as a chef at the Zazu's Kitchen across the road from the mural, said: "It's just mindless vandalism isn't it?
"It's a nice, well thought-out piece of art and someone has come along and defaced it."
The mural is painted on the side of bricked wall of Nurettin Sayin's barber shop The Point.
The 40-year-old, from Stokes Croft, said: "I was really upset to see it had been vandalised. It's one of the most famous paintings in Bristol and I've even seen people from Spain here to photograph it.
"They should clean it up and put it behind toughened glass so it's protected."
Just days after he daubed his work on a wall in Hendon last month, someone spray-painted over the word PRICE-LESS.
In January, it was revealed that the Mild, Mild West street art will be brought under cover as part of a new housing development.
Bristol City Council's development control (central) committee approved plans that will see the mural housed in a glassed cafe area in front of a new block of flats but some say the move will leave the art partially obscured from public view.