Can I tell other employees or customers why I had to let someone go?

The law does not prohibit you from telling third parties why you let an employee go.  However, if you work for a business or other employer, you should verify that such action would not be a reason for the company to fire you.  Additionally, you always run a risk that the employee would sue you for defamation.  So, while you might be able to do it, you should ask: should I do it?