Can a Funeral Home owner withhold your pay if as funeral director made a mistake in a contract with a family and the funeral home lost money.

Assuming you have no contract which provides otherwise, yes.  The funeral home is entitled to set the terms of your continued employment.  It has made responsibility for financial mistakes a term of that employment.  You don't have to agree, but if you don't the funeral home does not have to continue to employ you.  Moreover, the law is that employees are liable for any damages their neglicence causes the employer.  Many employers don't try to recoup these types of damages from their employees because it's bad for employee relations, but they do have the right to do so.