EDIT: Functionality, details
Earlier today we shipped some code for ping muting to PBE. We'll be turning it on for testing on PBE in the next few days, and hope to have it live around the world within just a couple patches. This is a new button we're adding to the tab menu. It'll axe standard, smart, and HUD pings from the player you ping mute.
The mute button that's already in the game is not moving or changing at all. It mutes chat, and extracurricular animations and emotes. The idea is to give everyone granular mute controls.