Head Keziah Featherstone told 14-year-old Jordan Ford his red mohawk haircut was unacceptable.
But the teenager accused her of double standards after he found a picture of Ms Featherstone with dyed purple hair and posted it on Facebook.
He wrote alongside: "This is not an example to set to other students."
The post attracted more than 50 comments but it got out of hand when many made reference to Ms Featherstone's weight.
However, school bosses at Bridge Learning Campus in Bristol accused Jordan of encouraging cyberbullying and demanded he apologise.
When the schoolboy refused, he was permanently excluded and reported to police.
Jordan's parents, mum Patricia Hedges, 43, and father John Ford, 46, have defended their son's actions and said it was clear they were 'looking for an excuse to get rid of him'.
John, from Bristol, told his local paper: "He found a picture of the headteacher with purple hair.
"This was after Jordan had been told to change his hair colour because it was banned by the school.
"His comment said something like: 'How do you expect us to follow your example if this is the example you are setting?'
"My wife went up to the school to see if there was any chance of him going back but because he is a bit of a clown they were looking for an excuse to get rid of him.
"We think it's unfair that he's been punished because he's the class clown.
"He dyed his hair red and the school made a really big thing of it but there are teachers up there with coloured hair."
Mark Davies, chief executive at the academy school, said the post encouraged other students to cyberbully a member of staff.
Mr Davies said: "Jordan and his parents signed a home school agreement in terms of acceptable use of IT, which is very clear.
"Even if it was in his own time, it invaded a person's private space and he copied pictures from a staff member's personal Facebook profile.
"He refused to take part in any restorative justice which would have involved meetings between him and Ms Featherstone.
"It was a permanent exclusion because he broke the contract between the school and student. His actions were against the morals of the school."
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