You can mute yourself and all other players throughout your multiplayer class.
From the Lobby and Results screens:
At both the initial lobby screen and at the results screen at the end of a class, you’ll be able to mute anyone, including yourself.
To do this, click on the name of the person you’d like to mute using the trigger on the back of your controller.
During a Class
If you’d like to mute players during a class then you’ll need to bring up the pause menu by pressing A, X or the Menu button depending on how you have this button configured.
From here you’ll then be able to mute players individually by using the trigger button on your controller.
NB: It’s not possible to pause a Multiplayer class. If you bring up the pause menu to mute individual speakers, the class will continue through this menu until you close it