In order to be able to turn off the Department when the Faculty Directory is printed, you will need to remove the Department designation from the Directory.
To do this, navigate to:
Core > Settings > Directories
Click the editing pencil on the Faculty & Staff Directory
Change Display and Group by from Department, to None
Users can still filter by the Department on the Directory itself, however, the Departments will not display when printed. With the Group and Display by Department being selected, this causes the Employees to display individually, AND in each Department they are associated with.