South Australian Premier Jay Weatherill says his Government will not cooperate with a Senate inquiry into the state's TAFE training crisis, describing it as a "stitch-up".

The State Government has set up an independent inquiry into TAFE SA after a scathing audit led to the suspension of 14 training courses, affecting hundreds of students.

TAFE SA's chairman Peter Vaughan has been sacked and chief executive Robin Murt resigned on Monday.

Federal Education Minister Simon Birmingham has referred the matter to a Senate inquiry to investigate the administration of "significant" federal funding.

But despite urging Commonwealth cooperation with a state-based royal commission into Murray-Darling Basin water theft allegations, Mr Weatherill said SA ministers and bureaucrats would not be giving evidence.

"We're not participating in a stitch-up for political purposes at a national level," the Premier said.

"We're happy to supply information to a Senate inquiry if they're carrying out a proper exercise but we're not going to participate in the exercise Senator Birmingham has in mind.

"Mr Birmingham has decided to play politics with some of the difficulties with TAFE and of course we're not going to cooperate."

The State Opposition wants to reconvene Parliament so it can ask questions about TAFE's management.

"Parliament must be recalled, we must get to the bottom of this and have it resolved," Deputy Opposition Leader Vickie Chapman said.

"This is a scheduled optional parliamentary sitting week and we are ready to go in the Opposition to bring this issue back to the Parliament.

"We're satisfied now that there's been a cover-up in respect of the mismanagement."

But Education Minister Susan Close said there was no need for Parliament to reconvene.

"I just can't see how people sitting in Parliament is going to help TAFE, is going to help TAFE students," she said.