How to Mute Direct Messages and Channels in Slack

If you mute a direct message, you'll no longer be notified of new messages from that conversation. Muting a DM will not mute all messages from a specific teammate when they're posted to other conversations. 

• Open the Conversation or Channel you’d like to mute.

• Click the three vertical dots (ellipsis) in the top right.

• Click  Edit Notifications.

•  Select Mute channel/conversation. You can also choose to mute everything but mentions. If you choose Nothing you will not get notified even if someone mentions you.