This is possible only for certain stereo tracks. When the vocals
are exactly the same on both stereo channels, you can remove them
by subtracting one channel from the other. This works for many
studio recordings, where the vocal track is mixed exactly in the
center.
To do this in Audacity:
Import your stereo file into Audacity.
Open the track menu (click the arrow next to the track title), and
choose Split Stereo Track.
Select the lower track (the right channel) by clicking it in the
area around the mute/solo buttons.
Choose Invert from the Effects menu.
Using the track menus, change each track to Mono.
Press the Play button to hear the results. If you are lucky, the
voice will be gone but most of the other instruments will be
unaffected, just like a karaoke track. You can use the Export
commands in the File menu to save the results.