The TES Scotland also understands that Mr Mitchell's "dismissive" and "confrontational" attitude has been reported to Ross Finnie, the Liberal Democrat Environment Minister and a key local party figure. The Liberal Democrat victory over Labour in May's council elections was hailed as a fresh era for local government.
The Roman Catholic Church is also angry with Mr Mitchell over his refusal to honour the previous administration's pledge to build a denominational primary in Wemyss Bay.
This has become a casualty of the new council's decision to pull out of an pound;80 million investment package for schools to be funded through a public private partnership (PPP), despite enthusiasm for it by Liberal Democrat ministers in the Scottish Executive.
The Headteachers' Association of Scotland has now been forced to step in to defend its members against what they claim are Mr Mitchell's misplaced criticisms of schools in Inverclyde. It has written to Alan Blair, leader of the council.
The education convener himself was robustly dismissive of the allegations against him. He told The TES Scotland on Monday: "Half are lies and half are merely opinions." He ended by assuring us it was a lovely day in Greenock.
Tony Sweeney, who chairs the Greenock High school board, said that school board members who had attended a meeting with Mr Mitchell left "shell-shocked". Mr Sweeney added: "We could see education policy imploding in Inverclyde."
One head said colleagues were "aghast at his belligerence and tone" at another meeting, describing the effect as one of "jaws hitting the floor".
Another accused him of undermining the work of the council's own education officials. While other councils have been given higher ratings since HMI reported on Inverclyde in September 2001, it remains the only authority in Scotland to have received a 'very good' score for its record on continuous improvement.
Mr Mitchell, asked about allegations that he was not on the side of teachers and schools, replied: "I'm not sure I'm interested in denying them."
He added: "I said I would tell them the truth, that I was not going to flatter them and that I was not going to speak in platitudes. Despite the HMI report, I said Inverclyde faced very serious difficulties in educational terms.
"If they don't like the truth, there is nothing I can do about it. If they don't like me, there is absolutely nothing I can do about it."
Did he feel he was being treated unfairly or receiving a hard time? "I don't suffer from paranoia," Mr Mitchell replied.
He also answered claims that the Liberal Democrat administration had abandoned the PPP programme while putting nothing in its place. The previous scheme envisaged shutting 13 primaries, one secondary and a special school in return for building six new primaries and refurbishing every other school.
The new plans involve the closure of five or six primaries and the use of conventional funding to refurbish the others, a process that could take up to 10 years.
But the convener repeated earlier assertions to The TES Scotland (May 16) that the previous PPP scheme was "a bad deal which would have given us pound;80 million of capital expenditure and cost us pound;383 million over 30 years". He said it made no sense to tie funding into schools which may not be needed in the future, as Inverclyde rolls fall by around 200 a year.
Mr Mitchell suggested that Liberal Democrat ministers in the Executive are simply going along with PPP because it is part of the coalition agreement with Labour.
"The Liberal Democrats in England are hostile to PPP. In Scotland, we are neutral: the official party position is that each local authority must decide for itself."
THE CASE AGAINST
Among the charges Jim Mitchell faces are:
* Dismissing the consultative procedures for school closures.
* Suggesting the education department put too positive a spin on the favourable HMI report on Inverclyde.
* Describing teachers as employees "like binmen".
* Denying teachers are protected against compulsory redundancy.
* Taking a negative view of pupils with special educational needs - he calls them "disabled".
* Telling heads four times in one meeting that he knew nothing about education.