An academy trust is looking at closing its design technology and computer science departments, which will "disadvantage non-academic students", unions say.
Documents seen by the BBC show the Inspiration Trust is consulting staff at Great Yarmouth Charter Academy (GYCA) on getting rid of eight posts.
The trust, which hit headlines over its ban of extreme haircuts and "strict" rules, confirmed it was "reviewing staffing".
The move would save £385,000 annually.
A total of eight possible teacher redundancies are noted in the document; four in design and technology, two in computer studies and a further one each in Spanish and EAL - for children being taught English as an additional language.
As well as the loss of teachers, unions are worried support staff would also go as a consequence.
National Education Union (NEU) spokesman Bob Groom said the plans were "very disappointing".
He said: "When you take the opportunities for children in the area, these are going to be vocational, with many looking towards apprenticeships in the off-shore and energy sectors in the Great Yarmouth-Lowestoft corridor.
"Design technology subjects like resistant materials are expensive to run, but non-academic children are being disadvantaged here."
A spokesman for the trust said it regularly reviewed staff structures, to "ensure that we best reflect the needs of our schools and our pupils".
"We are currently consulting with staff at Great Yarmouth Charter Academy on some proposed changes to help ensure that we have the right roles for the future," he added.
The document reveals the GYCA is forecasting a deficit of £85,000 in 2017/18, predicted to increase to £339,094 in 2018/2019 and £434,550 in 2019/2020.
It said this was "due to a significant fall in pupil numbers" from 805 to 680 between September 2017 and January 2018, with a further fall expected in September.
Figures released by Norfolk County Council for the September 2018 year 7 intake reveal that of 175 available places at the school, only 134 had been taken up.
Inspiration Trust also runs the nearby free school Trafalgar College, where a fiercely-opposed merger between it and GYCA is seeking government approval.
Only 25 out of a possible 120 year 7 places have been allocated for Trafalgar College.
Locally, all the high schools are more or less at capacity for this September's year 7 intake with only Flegg High having a high vacancy rate of 32 spaces.
Inspiration Trust, which runs 14 free schools and academies in Norfolk and Suffolk, received praise from Ofsted inspectors following a snap inspection last month at GYCA.