The National Association of Schoolmasters Union of Women Teachers said it would also be prepared to strike to force heads to stick to the agreement.
Funding problems are "no excuse" for schools which fail to meet their legal obligations to reduce the burden on staff, says a handbook sent to members.
Chris Keates, the union's deputy general secretary, said: "We cannot have the implementation of the agreement undermined by schools letting staff go and not replacing them. This is not an optional extra.
Refusal to implement the agreement would be like refusing to implement the national pay award."
The move puts the NASUWT on collision course with the National Association of Head Teachers which has pledged to pull out of the agreement unless ministers make more funding available.
In a letter to The TES earlier this month, David Hart, NAHT general secretary, warned: "For many schools, it is not a question of spending resources either on workload reduction or other vital priorities. They will be struggling to find any additional cash at all."
The NASUWT warning is the latest sign of tension among unions over the deal, which is due to come into effect next week.
The National Union of Teachers is the only classroom union to have refused to sign the deal. It opposes teaching assistants being allowed to take whole classes.
Signatories to the agreement hope teachers will benefit this term when 24 routine and administrative tasks are transferred to support staff.
The handbook instructs members not to perform these tasks even if they enjoy them. It says that this could "undermine the whole agreement and allow a return to the current workload situation."
It adds: "The agreement heralds a major change in the culture of schools which should not be dismissed as just another initiative."