Can I remove a peice of drywall without damage?

It's very unlikely that you can remove it without damage. If you're lucky, you might get it out with little enough damage that you can spackle it later, unless you have walls like mine with a vinyl textured wallpaper which is hard to spackle successfully since the texture is different on the patch. And as you may know already, they sometimes use odd sizes of drywall in mobiles so it might be hard to get a replacement sheet the right thickness. I couldn't find one. It might end up cheaper to replace the drywall on the whole wall than to pay the exorbitant prices they ask for the odd sizes if you can even find the one you need.

Is what you're mounting so incredibly heavy that you can't use hollow wall mounts of some kind? Or can you put a board across so it hits two studs and then mount whatever it is onto the board?