Android 5/Lollipop did away with the volume rocker push down to mute your phone mode in favor of the new Priority Mode from Google. Does the Galaxy S6 and S6 edge use that new Android 5 Priority Mode, or did Samsung include a mute-mode?
You can mute the S6 and S6 Edge with the volume buttons. Samsung has been incorporating this in the most recent Lollipop builds for several of their devices.