I regret to say that you cannot remove deep scratches just by rubbing with a bit of sandpaper (shudder) and a couple of different cutting pastes. Sure it will remove paint left on from other cars may smooth out clearcoat scratches, but once the base paint is exposed it needs repair, be that touch up and clearcoat or professional work.
An alternative for small chips that many have used with success (inc. me) is the
http://www.langka.com/ where in essence you touch up the scratch with normal BMW paint and then smooth out the resulting repair prior to normal polishing and waxing. Again designed for small damage not deep or long scratches.