Cutting out each nail or screw seems very tedious to me. Plus, you would have to support the drywall as the last few fasteners are removed. Cutting it in sections would help. Even so, you are going to get dust on everything below.
I would cover everything below with 2-mil plastic and cut it into sections and just pull them down. Since you must have attic access, remove the insulation first. It will be smelly and you won’t be reusing it.