When I've removed drywall, I've always marked it with a pencil, used a razor knife to score the straight lines on the edges, then top and bottom. Then go over the score lines 3-4 times, depending on the thickness of the drywall. Then I'd make an X score from corner to corner. A couple-3 passes on the X lines, then tap the center of the X with a hammer. It makes 4 nice triangular pieces that you can just pull out.
I try and work in square sections, so 16" on center studs, I'd make a 16" square. Then another below that, and another, etc... Little mess with the razor knife. I've tried it with an oscillating tool. The tool works great! But it does make dust compared to a razor.