As a new user I also had an extremely frustrating time trying to find the mute tool. The only one labeled "M" I could see was to mute/unmute all tracks. Not what I was looking for.
The solution is to hit F10 to toggle between the Erase Tool and the Mute tool. F8 & F9 also click thru some tools on the buttons just to the left of the erase/mute tool (whatever those do).