Block texts in Messages on Mac
If you use iMessage to send text messages, you can stop receiving text messages from certain people.
In the Messages app on your Mac, choose Messages > Preferences, then click iMessage.
In the Blocked pane, click the Add button and enter the iMessage address you want to block.
Tip: On your iOS device, block text messages without creating a new contact. See the Apple Support article Block phone numbers and contacts on your iPhone, iPad, or iPod touch.
If you’re receiving email messages you don’t want, you can manage them in the Mail app. Just create a rule in Mail that automatically moves emails from people you specify to the Trash or another mailbox. See Use rules to manage emails you receive in Mail on Mac.