No, removing wallpaper with vinegar cannot damage the drywall. In fact, vinegar is one of the best natural products available which is very useful in removing wallpaper without much effort and most importantly, without any damage to the drywall. A vinegar and warm water solution is used to remove wallpaper from drywall. Dip a sponge in the vinegar/water solution and squeeze gently. Water should not be dripping from the sponge. Now, soak the wallpaper with the solution by moving the sponge over it in a downward motion. Wait for a while and peel off the wallpaper from the wall, while it is still wet. The wallpaper paste will also come off along with the peeled wallpaper.