Presumably you don't want any chance of loosing lose sync of the audio you keep with your video, so any un-grouping or cutting should be avoided. I'd suggest:
Right click on your audio track, choose 'Display track curves' and you'll see white (L/R stereo?) and bright green (volume) lines appear. A double click on the green one should produce a little box which can be dragged down to reduce the volume to nothing at the bottom. To mute a section you will need four control points -- the start and the finish and two more. If the the inner two are close by the ends you can have an immediate reduction or if they are placed further away the sound can fade out/in more gradually.
The 'sound of silence'? To fill in the gaps place (pieces of) an audio track underneath the original and repeat the volume curve exercise to silence all but the sections that replace what you have removed. If you take care to match downward slope line of original audio with an upward slope line of a replacement you should get a smooth audio cross fade. Note cuts and object overlaps will also make the fades but, as cautioned above, you might move something out of sync by mistake.