As it says on http://manual.audacityteam.org/o/man/tutorial_vocal_removal_and_isolation.html , the “make mono and invert” trick only works on vocals that are panned centre without stereo reverb, which is rarer than it used to be.
For vocals that are not centre-panned, you can try the plug-ins on http://wiki.audacityteam.org/wiki/Vocal_Removal#Windows_VST_Plug-ins or try the 2D Stereo Toolkit plug-in. If you try the Toolkit, put its NY file in the Audacity Plug-Ins folder then restart Audacity.
Or look for a karaoke version of the song on the internet.
Since you posted in “Adding Features”, are you requesting a built-in Vocal Remover that works on more than centre-panned vocals?
Gale