Frank Thomas has resigned from Capital City academy in Brent, north London, and is expected to leave the school at the end of term.
There are claims that the school needs to save pound;300,000 and will make seven teachers redundant. Mr Thomas was not available for comment when contacted this week.
The academy was opened last year by Tony Blair, who returned two months ago to unveil ambitious rebuilding plans for every secondary school in the country.
The 840-pupil specialist sports college, designed by architect Sir Norman Foster and sponsored by advertising agent Sir Frank Lowe, was built on the site of the former, failing Willesden high.
A spokeswoman for the school said that the resignation and the need for job cuts were "not related" and denied that the school had financial problems.
The school had been set up with a management team of 15 senior staff now considered "too cumbersome and top-heavy".
Staff have voted for strike action to prevent the job cuts, but talks between the school governors and the National Union of Teachers over saving the posts are continuing.
It is understood that the school is having to to save money to cover maintenance costs and anti-vandalism measures. But the precise reasons for the cuts are not known because the seven governors have not yet met the eight sponsor-board members, union representatives said.
Hank Roberts, NUT branch official, said: "It is extraordinary that the school is facing financial problems after all this money has been spent.
"If it had been spent on the old failing school it could have been one of the best-equipped schools in the country without any need for upheaval."
The first year of the academy's existence has been plagued with problems.
Up to 20 teachers are thought to be leaving this year amid complaints of excessive workload and the "exhausting" building design.
The unusual layout features a shopping mall-type corridor, but teachers are annoyed that there is no staffroom and say the lavatories are poor quality.
A spokesman for the Department for Education and Skills said:
"Academies operate in the toughest areas. They sometimes have to take tough decisions in the interests of raising standardsfor pupils."