Anything that does partially remove vocals usually uses some kind of phase reversal as mentioned above. This will basically make the other backing instruments and rhythm sound completely different and probably pretty horrible. It will still be the same song, but it will sound much worse.
If you want to try it out, this sometimes works. Invert the phase of either the left or right channel, it won't totally remove vocals, but it sometimes makes them soft enough to not notice, although it will affect all other instruments in the same frequency range.