When a student leaves your school, in addition to entering a Leaving Date on the student profile, you need to off-roll them in order to remove them from the register and appearing as a current student in reports.
On the student profile's extended tab, scroll to the base and click on Off Roll.
You will then be asked to enter a Leaving Reason. Choose the relevant one for the student and click Complete Off Roll.
This student is now off-roll and will not show in registers. You can access former student profiles if you go to Admin > Students > Search Not On Roll.