When you mute a group conversation in Instagram Direct, you'll still be included in the conversation but won't get notifications from it. To mute notifications from a group conversation in Instagram Direct:

Instagram app for Android and iPhone
Tap

or

in the top right of Feed.
- Tap the group conversation you'd like to mute.
- Tap the group name at the top, then tap next to Mute messages or Mute video chat.