Seventy per cent of union members backed strike action at the school which has been forced to make cuts after running up a deficit of more than £1m was last week labelled the first academy to be labelled a failure by the education watchdog Ofsted which said it had not provided "an acceptable standard of education".
Chris Keates, general secretary of the National Association of Schoolmasters and Union of Women Teachers, said cutting staff would not improve the situation.
Joe McCarthy, chairman of the Unity City academy trust, said nine of the 10 job losses had been resolved without compulsory redundancies.
"Industrial action is the very last thing we need at this critical stage in the development of the academy. It would benefit nobody," he said.
Last week Ofsted inspectors listed a number of weaknesses ranging from "fragile" leadership, an inappropriate futuristic building and a staff absence rate so high that up to a third of teachers regularly failed to turn up. The Department for Education and Skills said it was disappointed by the union's decision and said Unity would be working closely with the nearby Macmillan city technology college in a bid to raise standards.
