iOS 7 comes with the ability to block sender. When you add a contact to the blocked list, you will not receive phone calls, messages or FaceTime from that contact. If you’ve setup FaceTime and iMessage on your Mac, the blocked list will apply as it is going through the same Apple backend.
With the release of OS X Mavericks 10.9.2, Apple added the ability for you to manage this blocked list directly from your Mac. Before that you can only add or delete blocked senders in iOS 7.
To manage the blocked list on Mac, go to Messages app > Preferences. Click on “Accounts” tab, select the iMessage account, and then click on the “Blocked” option.
Click on the “+” and “-“ button at bottom to add or remove a contact to the blocked list. If the person you want to block is not in your contact list, add their phone/email detail manually to the Contacts app first.