It sounds like you are trying to assemble an ARF or a covered kit. If you are just trying to remove an area so you can install the elevator carefully use a soldering iron to cut the coveing at an appropriate point. Once you get it started you can lift the covering slightly from the wood and cut with a new blade. Be sure you do not cut the wood. After removing the desired section, re-iron the remaining covering.

Question - do you need to remove the covering from both the top and bottom of the elevator? In many planes you do.