How do you remove audio from video to keep the video using vlc?

The way to remove the video from the audio (and only retain the audio) is by dragging the video clip to the MUSIC/AUDIOtrack in the Time-line view of Windows Movie Maker instead of the Video track.

Once you have the audio there, publish/finish it. That will change the video to an 'audio' format (in this case a .wma).