The mural was also daubed with red paint earlier this year
A second mural in central Bristol by the graffiti artist Banksy has been defaced.
The Mild Mild West, which depicts comic policemen and a bear, has been splattered with blue paint.
On Monday, a picture painted on the side of a wall in the city's Park Street was vandalised with blue paint splashes.
The image, which was due to be restored on Wednesday, shows a naked man hanging from a window sill.
Businessman Albert Murphy, Conservative councillor for Avonmouth, said he was using his own cherry picker to clean the Park Street work.
"The council won't do it because they haven't got the facilities to do it and we have.
"We're going to remove the biodegradable paint first and then it can be cleaned off with soapy water and then we'll start on the picture.
The mural was also sprayed with red paint in April
"I'll do it myself, there's no cost to the council whatsoever."
In April, the Mild Mild West was sprayed with red paint by a group called Appropriate Media as a protest over the Stokes Croft area of the city "being gentrified"
The red paint was later cleaned by community volunteers.
The Mild Mild West was voted Bristol's favourite alternative landmark in an online poll in 2007.
Bristol City Museum and Art Gallery is showing an exhibition of Banksy's work which is due to run for 12 weeks.