Iffy. It's not totally inconceivable, but there will almost certainly be some loss of quality, and you might not be able to get rid of the other sounds completely.
FFT analysis can analyze a segment of sound as to what frequencies are present in it, and it is possible to take that analysis and take out the lesser frequencies, i.e., sounds and talking where the energy is spread among different frequencies, as opposed to music, which is likely to be concentrated in certain frequencies. Then it can be transformed back to audio, minus the frequencies you remove. There are other ways to filter frequencies out too, but it's always dependent on having some idea what frequencies you want to keep and what you want to lose.
At any rate, it's never cut-and-dry. Just like you are able to hear numerous simultaneous sounds with only two ears, all the talking and music is mixed into one single track. The only exception might be a special edition DVD or what not with "audio options". Actually, even if there were a track of the audio somewhere with *just* the dialog and sounds and no music, you could take the difference and have the music.
I've been learning a lot about signal processing and FFT and digital audio, but I've never actually tried to do something like this. Would you like me to see if I can do anything with it? PM me if so.