A great way to cut drywall is to use a utility knife (and a straightedge) to cut through the first paper layer (and into the gypsum a little as well). Then with a quick snap with your hands, you can break the gypsum right at your scored cut.
The wall board will now only be held together by the other paper sheet. You can bend the board to something like 90 degrees, and use your utility knife to free-cut the remaining paper backing and you are done. The 90 degree angle guides the blade so you don't need to use a straightedge for this cut With a little practice it becomes surprisingly easy. I cannot believe that I used to cut drywall with a jigsaw before.