Understood but, The cost of a sheet of drywall vs. the effort of trying take it off intact plus the need to store it plus the repairs you will have to do to use again plus the size of the pieces you will be able to save. I have tried this and have given up on worrying about it. I have had some success with saving the lumber and using it for various smaller projects...if it is not too old.
A few additional thoughts: Since you said it is a basement, we can assume it is a concrete floor and not the joists in your diagram. The sole plate will probably be fastened to the floor and you will have some damage to repair there. If it is a finished floor (some kind of floor covering), does it extend under the wall? if not, you will need to find a way to patch it or replace the existing floor.
I'm not trying to scare you off the project, just giving you some things to think about before you begin.
Learn something every day