I do not know of any "Fire" button or functionality, but you might want to set the employee to inactive. He/she will no longer show up with any overviews etc. but will still be in the database for historical purposes. I.e.: The employee will not be deleted.

The only downside to this is that you can no longer reactivate and/or view any information on the employee and in order to make him available again, you would need to run a query on the database, setting active = true.

An alternative would be to use the contracts module where you can define the length of the contract. It will not hide the employee, but it will at least tell you information about the current employee status.