Mute email conversations in Mail on Mac
If you receive email messages, such as in an active conversation, that are more inconvenient than useful, you can mute them. If you change your mind later, you can easily unmute a conversation.
Mute conversations
In the Mail app
on your Mac, select the conversation you want to mute.Click the Mute button
in the Mail toolbar (you may need to first click the More Toolbar Items button 
). The mute icon appears in the conversation’s messages in the message list.
The conversation stays in your Inbox but you aren’t alerted by a notification or sound when new messages in the conversation arrive.
You can set an option in Mail General preferences to automatically move a muted conversation to an archive or bin mailbox, depending on which one is available for your email account. Future messages in the conversation go to that mailbox instead of your Inbox.
Unmute conversations
In the Mail app
on your Mac, select the conversation you want to unmute.Click the Unmute button
in the Mail toolbar (you may need to first click the More Toolbar Items button ).The mute icon is removed from the messages in the conversation.
If you set the option to move muted conversations to the archive or bin mailbox, the conversation remains in the bin after you unmute the conversation.