This was discussed in bug 634329, and it was decided that a mute button is unnecessary.

Giovanni, can this feature be added as an extension then ? I'll be interested in develop such feature if gnome-shell designers don't want this feature.

Techically, it is possible but you need to replace the whole sound menu (declare it in the extension and set Panel.STANDARD_TRAY_ICON_SHELL_IMPLEMENTATION['volume']).
This said, I don't think that a mute button is so useful, given that in most cases you have an hardware mute key, and if not you can set a keybinding, in case you need to disable sound immediately. But I like to say "code first, design later", so I have no problems with including this.

The easy way to do this would be to extend the volume bar's reach to both the left and right of the bar itself, so that clicking on the empty space bring the volume to the minimum.

It would also make it finger friendly, which is always a good thing.

Created attachment 186435 [details] [review]
PopupSliderMenuItem: intercept clicks outside the slider

Connect to button-press-event on the menu item actor, not on the
slider, so any part that is highlighted is also clicked. This means
that click on the left of the volume slider is a rapid way to mute.

Comment on attachment 186435 [details] [review]
PopupSliderMenuItem: intercept clicks outside the slider

doh. wish I had looked at the patch before 3.0.1. we could have gotten this in.

Attachment 186435 [details] pushed as d104f92 - PopupSliderMenuItem: intercept clicks outside the slider