Duke William of Normandy won the battle because was well prepared and had a good army. They prepared carefully for the battle. The Normans had knights on horseback who were skilful fighters.
A utility knife, metal ruler, and a hammer can be faster than trying to carefully saw an opening. Score the drywall a couple times till you are most of the way through, then just knock a hole with the hammer and break the drywall back at the score lines.
When you need to cut inside corners, cut one side with a drywall saw. Then score the other side of the drywall with a utility knife and snap it back as you would any other cut. Bend the back panel away from the score line to break it along the score. It is usually easier to snap the panel away from you.