If the mix have the vocal centered, and no other backing vocals or reverb effects on the left and right, there is maybe a way.
But most recordings are not like that exept early demos of bands, or maybe early albums by Bob Dylan, lol!
The trick is: the invert method.
You separate the right and left audio in, lets say, Audacity. Then you change them to "mono".
Then you invert one of them: "effect/invert"; This will invert the frequencies of this track, so everything that is exactely the same in the other track will be muted. Then you save this to a mono file. (if I made a mistake, please someone correct me).
But like the others said, it is very unlikely that it would work.