Either tearing it off in as big of chunks as you can keep it in OR taking a sawzall down either side of the stud and taking it out in 4'x14.5" pieces. The later is easier becasue you get rid of all the big pieces and only have to clean up little pieces but you need a sawzall and you have to be VERY carful around wires and pipes.
Is the drywall nailed or screwed on? I removed a lot of basement drywall that was nailed in place and found the best (not necessarily the fastest, but certainly the cleanest) way to do it was to remove all the nails I could find using a Dasco Pro double ended nail claw bar (Home Depot or Lowes) that was tapped under the nail with a hammer. To find nails buried in compound, I tapped the compound with the edge of the hammer head. This would generally exposed the nail... surprising how easy it was to find the nail pattern that the installer use. If I could get 50% or more of the nails out, the whole piece could generally be removed in big pieces with minimal dust and debris. Once removed, I used a box knife to immediately score and break the piece into smaller pieces for easy disposal.
There is no "clean" way to demo drywall. Knock a hole and start tearing it off the studs. Hope it isn't glued, but I recommend glue when you replace it. If you sawzall down either side of the stud (time consuming and dangerous) you still have a strip of drywall ON the stud that has to be pulled off...
When I have to remove drywall and keep the mess to a minimum I start at a corner and cut it with sawzall, once it is cut I don't try to just rip it off, I have found that if I get a vibration ( sorry only way to describe it) going it will usually pull the sheet free from the next stud. Then I can remove an almost full sheet of drywall, assuming ( sorry bad word) that it was not glued.
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