Block callers in FaceTime on Mac
If you don’t want to receive FaceTime calls on your Mac from certain people, you can block them. Then, if they call, you’re not notified and the call is not answered. You can call a blocked caller without unblocking them.
Important: If you block a caller on your Mac, the caller is blocked on all your devices where you’re signed in with the same Apple ID. See the Apple Support article Use Continuity to connect your Mac, iPhone, iPad, iPod touch, and Apple Watch.
In the FaceTime app
on your Mac, choose FaceTime > Preferences, then click Blocked. Click the Add button
, then select a name in the list of contacts.You can also use the call list to block a caller. Control-click the contact in the list, then click Block This Caller.
To unblock a caller, select a name, then click the Remove button 
.
To block all FaceTime or phone calls, turn off FaceTime or sign out of FaceTime on each device. See Sign in to or out of FaceTime.
Tip: Another way to prevent unwanted callers from bothering you is to set up communication with your contacts only.