How do you punish an employee who made a mistake that affected the company negatively?

the mistake that affect the company negatively should be faced by a strong punishement even it reach to fireness

It depends on the nature and impact of act. (its a mistake or intentional/deliberate act, behavioural or operational, most importantly how much it affected the company). Please be specific for a better answer.   

P.S : Punish is strong word to use specailly for a mistake. 

It is interesting to note that communication is the key factor in any successful disciplinary process.  A useful model for communication is the concept of progressive disciplinary approach of stiffer penalties for more serious violations and increasingly more serious penalties for repeat offenses.   So, for different degrees of fault, there are different degrees of punishment to deal with offenses. Tools to respond to offenses include: for minor offenses: communication of the standard, disapproval or a verbal warning may be suitable to use, but for moderate offenses, it may be appropriate to issue a written warning, and in case the offense is serious may be suspension, investigative suspension or termination are more appropriate actions.  

But, I must say that before terminating an employee, we should listen to his or her side of the story first, he or she must be given an opportunity to explain, because he or she may have had a very good reason for his or her behavior.  Permitting employees to explain their perspective first is the most important principle in employee discipline, because it will save the supervisor from destroying employees trust, prevent the supervisor from looking foolish in the eyes of employees, and it helps to reduce high tensions and emotions in the work place.  

Of course, there is a call for providing privacy in these cases, but we need to balance privacy with the requirement to protect the company and employees’ safety and reputation.  

But bear in mind that, terminating an employee in haste or on the basis of fuzzy evidence can cause more problems in the long run than the ones you think you're solving.  In these cases, it's better to try to turn the employee around than go through the painful firing process, unless the person has committed acts that are clear grounds for immediate termination, such as impropriety, gross incompetence, or theft.   Thank you