There is no easy way to remove the vocals off a Song.
You have to rely on the fact that the Music is Stereo and the Vocals are mono.
When this is the case, there's an 80-90% of of removing the vocals.
But as we all know, most vocals are packed with FX that work in Stereo, therefore the Software cannot cancel it out properly.
I imagine there's extremely intelligent software out there to be able to decifer vocal parts, delete them, and then do a "smart" refill of any instruments that happened to be playing in the same frequencies.
This would be something used in a forensics lab I'm guessing. I haven't found commercial software that can do it.
BTW, when you hear a "remix" what you actually hear is a very close facsimile of the original song. Basically some guy listened to the song, and being a musician with synthesizer knowledge (like yours truly) can patch up the same tune to sound 95% similar but without vocals.
Samplers help tremendously in this task.