There is also “Melodyne” (if your pockets are deep enough).
Within certain technical limitations, it is possible, though it is difficult to provide an easy to use interface for the task.
If the copy of the sound that you want to remove is identical (on a sample level basis) to the sound that you want to remove, then it can be “subtracted” by inverting, scaling to the appropriate level and panning to match the original.
Example 1:
Track A (original) has unwanted sound in left channel only.
Track B has the (identical) isolated unwanted sound (mono).
What you would do is to make Track B into a stereo track (2 channels) with the sound, inverted, in the left channel, and silence in the right channel. Then mix (“add”) Track A with the new Track B.
Example 2:
Track A (original) has unwanted sound centre panned.
Track B has the (identical) isolated unwanted sound (mono).
Invert Track B and mix with (“add to”) Track A. Audacity will automatically convert Track B to stereo because it is being mixed with a stereo track. Thus Track B, when inverted, is the negative of the unwanted sound.
Similar operations can be performed when you have an identical, isolated copy of the sound that you want to remove, wherever it is panned in the original stereo track. All you need to do in this case is to find the necessary pan position and scaling factor (though that is easier said than done).
There is a plugin called “Channel Mixer” that allows you to manipulate the level and mix of the left/right channels: http://wiki.audacityteam.org/wiki/Nyquist_Effect_Plugins#Channel_Mixer
Installation instructions: Missing features - Audacity Support
When working with sounds that are not identical at the sample level, then the task becomes very much more difficult. However there is an FFT based plugin called “Stereo Tool Kit”: Karaoke, Rotation, Panning & more
Installation instructions are the same as for other Nyquist plugins (see previous link).
Note that this is an experimental plugin from Robert J H. Notes about how to use it are in that topic - if you need further information about that plugin, please post to that topic.