Actually it is possible, but you need a copy of the soundtrack mix by itself first. Basically you invert the music and layer it over the full soundtrack. Unfortunately it is usually too hard to get an exact copy of the soundtrack. Another downside is, unless you had a 5.1 mix of the music, the output would be mono.

A similar technique can be used to remove watermarks from images and video.

I haven't used either technique in over four years so I won't be much more help; I might have another go at it this weekend to refresh my memory.