For purse lining slip seamripper into seam gently cutting to making hole. Turn lining out, use sharp end of seamripper and slip it under thread and pull cutting the thread.
You can pick up a cheap seam ripper and use it to carefully cut through the stitches to remove the lining. Most of the time the lining is sewn directly to the outer fabric so you may have to make hems when you're done.
Other than taking the seams apart and removing the lining, trim as close to the seam as you can and pull out the lining. Doing it the latter way will save you the time of sewing the garment or purse back together.
