After failing to win a place on the Gers' board at Thursday's annual general meeting, former oldco director Murray claimed Stockbridge has behaved "unacceptably" since joining the Ibrox board in June last year.
The one-time Blue Knight launched a stinging attack against the 39-year-old chartered accountant as he rounded on financial results that saw the club lose £14.4million in the 13 months up to June.
He also rebuked Stockbridge for leaking video footage of former chairman Malcolm Murray - one of Paul Murray's fellow "requisitioners" - appearing to be drunk onto the internet.
And Murray also repeated an opinion voiced by lawyer Richard Keen QC three months ago during a hearing at the Court of Session that Stockbridge and former board colleagues may have broken the law by trying to block the requisitioners from putting their nominations to shareholders at an AGM.
Murray told BBC Radio Scotland's Sportsound programme: "Putting aside Rangers and the history of this whole thing, if this was any other organisation, the financial mismanagement in the last 12 to 15 months which has been there for all to see, the personal conduct - to take a video of Malcolm Murray and upload it onto YouTube - is obviously unacceptable.
"Also when we went to the Court of Session, every member of that board committed an offence under the Company's Act. A pretty serious offence.
"So on all those bases, Brian Stockbridge's position is completely untenable.
"Now if the board of Rangers, including the new directors, including (chief executive) Graham Wallace, think that is acceptable then I think that reflects very badly on them."
Murray and his three associates - Malcolm Murray, Alex Wilson and Scott Murdoch - all failed to get the necessary backing from the powerful institutional investors as they were routed by the current board.
Stockbridge was left in no doubt about his lack of popularity amongst fans as he was roundly heckled during the two-hour meeting at Ibrox but still clung on to his job with 65 per cent backing.
And Murray admitted he may have paid the price for backing down on calls for an extraordinary shareholder meeting during the summer when the ruling regime were floundering.
"Starting with the voting result, I'm obviously very disappointed," he said.
"We could have called an EGM earlier this year] but took a decision that a bit of compromise was the best way forward the club. Hindsight is always a wonderful thing.
"But since then, the board has been able to get in a couple of credible directors, particularly Graham Wallace.
"And the one thing you have to remember is that institutional investors do like to support incumbent boards. They have supported what they see as a competent board to go forward and we have to accept that."
Murray admits he now fears for the Scottish League One outfit's future ambitions on the pitch.
He said: "Probably the most surprising revelation was that Graham Wallace said that the cost base would have to come down going forward and indeed they would be spending less money in the SPFL than they were in the third tier of Scottish football.
"So you start to wonder about how the team might look in a couple of years' time.
"Whatever happens, we have brought all the issues to the fore, we have got transparency to what is happening to the club.
"Fans effectively have been duped - to use a famous word - into buying season tickets over the last couple of years - they won't do it again unless there is proper trust and transparency."