The normalizing slider makes the volume of all clips equal, and you then can adjust the volume of all clips at the same time to make them softer or louder as a group. It will not remove all sound unless to make it so. As Ian says, you must move the slider very slowly.
Another way that you can do this is to use the Paste Adjustments feature. Select the first clip in the range of clips and adjust its volume to the level that you want. Then do Edit/Copy. Then select the remaining clips as a group and do Edit/Paste Adjustments/Volume. The volume level that you selected for the first clip will be pasted into the remaining clips in the group.
If the above two methods do not work satisfactorily for you, then your only other option is to manually adjust each clip to the volume level that you want.
-- Rich