The Unexpected Ring
macOS and iOS are deeply integrated through a suite of features known as Continuity. One of these features allows you to receive cellular phone calls from your iPhone directly on your Mac. When your iPhone rings, your Mac will automatically launch the FaceTime application and ring simultaneously, popping a notification onto your screen. While convenient if you are wearing headphones at your desk, it is highly disruptive if you are in a quiet office environment, sharing your screen during a presentation, or simply trying to focus without your computer blasting a ringtone every time you get a spam call.
Severing the iPhone Call Link
To silence your Mac and stop macOS from automatically opening FaceTime when your iPhone receives a call, you must disable the specific Continuity feature linking the two devices.
Open the FaceTime application on your Mac (you can find it in your Applications folder or via Spotlight search). Once FaceTime is open, look at the very top menu bar of your screen and click on FaceTime, then select Settings (or Preferences). Ensure you are on the General tab within the Settings window. Look down the list of options for a checkbox labelled Calls from iPhone. Click this checkbox to remove the checkmark. You can now close the Settings window and quit FaceTime. Your iPhone will continue to ring normally, but your Mac will remain silent and the FaceTime app will no longer automatically launch to intercept the call.