Just entering a Leaving Date will not off roll a student.
Pop to the extended tab of their profile and scroll to the very bottom. You will see a little blue button labeled "Off Roll" - click this.
You will then be asked to enter a Leaving Reason, so choose the relevant one for the student and click "Complete Off Roll".
This student is now off roll and will not show in registers. To find former pupils go to Admin > Students > Search not On Roll.