How to Delete a Department

Goal:

Go to Settings → Manage Locations
Select the Location the Department is housed under
Select the Departments tab
Select the beside the Department that you would like to remove
Choose Remove Department
You will be prompted with a warning message. If you're sure and ready to proceed, select Delete Department.

Only users with the Manage Locations permission will be able to do this.
Removing a Department is permanent and irreversible.
There shouldn't be any pending Requests under the Department you are about to delete, otherwise, it will not be possible to remove the Department. For more information see Can a Department be Deleted?