The current released version of JuMP (0.18) does not have the ability to delete variables.
This oversight is fixed in the upcoming release of JuMP. (Read more about that here.)
If you want to try it out for a spin, there are installation instructions at JuMP 0.19-beta released (JuMP/MathOptInterface). (Warning! It’s a beta!)
Once you’re using the beta, you can read about deleting variables in the new docs .