Seems that there is no way to mute the audio while capturing HDV footage at this stage…until FCP come with a plug in or something.
One option I found that works for me if when I filmed, I recorded on one channel only.
If the audio is recorded on your RIGHT channel then go in to the
system preferences > sound > output
and change the balance to the LEFT opposite of how you’ve recorded the audio on your footage.
That way you won’t hear the sound of your footage while you want to listen something else on your computer. But you will be able to listed in mono only. Its better than nothing ey?
Hope that this helped.
Mike