When you join an online match in Destruction AllStars, you're automatically placed in a party chat with the other players. Of course, not everybody wants to socialise. If you're not feeling up for a natter with some strangers, or if you don't want to listen to others having a chinwag, there is an answer.
While in the lobby, press the PS button to bring up the Activity Cards. The first one will be the party chat for the match you're in, and if you press square, it will mute all chat. You will need to do this each time you join a game, but it only takes a second.
Alternatively, you can join a party chat containing just yourself, and that way, the game won't automatically drop you into a party with other players.