Dismiss, Yes. Demoralize, No.
If you have to fire an employee, there are correct and incorrect ways to go about it. Some tips for successfully "ending the relationship" include using brevity, being compassionate, allowing the employee to respond, and calling security if the worker will not accept the decision. If the employee gets emotional, a box of tissues should help. It also pays to rehearse, possibly by using a mirror and firing your reflection.
See "Dismiss, Yes. Demoralize, No.", Matt Villano, The New York Times, August 7, 2005