Theres a number of ways you could do this, here is but a few:
One would be to split the track just before and just after the word (or sound) (Just as it sounds like you did in your fix), then right click on the clip you wish to eliminate and select >propertys>mute. Or you could just delete it if You wish, and then highlight the remaining clips and merge them back into one.
Another way would be to select the automation button for the track and roll the volume to zero just before the sound, and back to 100 just after.http://www.acoustica.com/mixcraft/v6/help/index.html
See "mixcraft reference>tracks>Automation"