This is quite easy to achieve in audition using the vocal remove effect from stereo channel extractor but a lot more difficult to achieve in audacity.
The way it works in Audacity is to create two mono tracks from the stereo track and roll the bass off one of the tracks. Invert one of the tracks and you’ll have the vocals removed as the inverted track vocals will cancel out the vocals on the ordinary track. The reason for the bass roll off is so there is no bass to cancel out when the two tracks are played together again.
In Audition you can set the central frequency, the width of the frequency and the amount of reduction which is a far more effective way of doing it.
BUT the effectiveness of doing this depends on how the track was mixed and mastered. Vocals are traditionally mono which is why they can be removed but the vocal effects applied will be stereo which is why they can’t be removed.
In short you’re never ever going to get a perfect result doing this. Some songs will work better than others. Your bass loss is because you inverted a channel with the bass still in the channel so when the two channels combine the bass also cancels out. Rolling the bass off one channel will wade that but there’s little you can do to remove the stereo effects added in the original mix of the tune so you’ll end up with some residual vocal.