If a group chat is getting too chatty when you're busy or just don't want to participate you can silence all the notifications by enabling Do Not Disturb mode on your iPad or iPhone. To enable Do Not Disturb for a particular group message or even a single contact, just open up the message thread in the Messages app and tap Details. From here you can enable the Do Not Disturb option to silence messages from that thread. To start receiving notifications for that thread again, just tap the same toggle switch to disable the Do Not Disturb feature.
You can leave a group conversation by tapping the red "Leave this Conversation" panel in the Details section of any group thread.