CakeHR does not allow you to delete active employees as we want to avoid any accidental data loss.
In order to delete an employee record, you first have to terminate it.
To do that, go to employee's profile & at the bottom of the page click on the red "TERMINATE" button. A window will appear where you can write in the details:
When employee is terminated, you will be automatically taken to "Terminated employees" report (it's under Reports > Employee data > Terminated employees) & from there you can click on "delete" icon next to each terminated employee.