An academy trust could close its design technology and computer science departments in a bid to save £385,000 a year.
The BBC has learned that the Inspiration Trust is consulting staff at Great Yarmouth Charter Academy (GYCA) on axing eight teaching jobs.
Unions said it would "disadvantage non-academic students".
The school, which banned extreme haircuts and had "strict" rules, said it was "reviewing staffing".
Four teacher posts in design and technology and computer studies are recommended for redundancy plus one each in Spanish and EAL - for children being taught English as an additional language.
National Education Union (NEU) spokesman Bob Groom said the plans were "very disappointing", with opportunities for children in the area tending to be vocational.
"Non-academic children are being disadvantaged here... with many looking towards apprenticeships in the off-shore and energy sectors in the Great Yarmouth-Lowestoft corridor," he said.
A spokesman for the trust said it regularly reviewed staff structures to "best reflect the needs of our schools and our pupils".
He added: "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."
Simon Gray, of the East of England Energy Group based in Gorleston, said the move was "contra-indicative of what's going on in the market place", and that ICT and computer knowledge were essential skills.
The document reveals that 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 reveals that of 175 available places at the school, only 134 had been taken up.
Inspiration Trust also runs the nearby free school Trafalgar College, which it is seeking government approval to merge with GYCA despite fierce opposition.
Only 25 out of a possible 120 year 7 places have been allocated for Trafalgar College.
Inspiration Trust, which runs 14 free schools and academies in Norfolk and Suffolk, received praise from Ofsted following a snap inspection last month at GYCA.