What quick and dirty tool/method should I use for cutting scrap drywall?
A craft knife or box cutter will do the job very quickly and cheaply.  You only need to score the front side of the drywall and then it should snap cleanly enough along the score line.

If you already have a Dremel or Roto-Zip, you can get drywall bits for them that will make short work of any drywall.