How to Block Someone on FaceTime
Apple's FaceTime application lets you make video calls to other FaceTime users. While there isn't a way to completely ban a user from attempting to place a call to you, there are a number of ways you can block a user from reaching you. If you want to block someone on FaceTime, you can do so by blocking his calls or by blocking your FaceTime connection entirely.
Blocking Individual Calls
Wait for the FaceTime call to be placed by the user you wish to block.
Tap the red "Decline" button on the iPhone's screen when the incoming FaceTime call appears.
Repeat anytime a call is placed by that FaceTime user.
Block All FaceTime Calls
Tap the "Settings" icon on the iPhone's home screen.
Tap the "Phone" icon on the iPhone's Settings screen.
Tap the slider to the right of the FaceTime heading on the Phone Settings screen to slide the slider to the "Off" position.