To remove someone you need to go to People > employee name > Person (dropdown) > Leaver. Then on the next page choose the date that they left the company and the reason for leaving. There is also a free text reason for leaving box.
Please note that you will not be able to remove them when they are a manager of a group - so change the groups manager if this is the case.
Once left they will be available in the leavers list in People > Leavers.