What is the level of the employee?
Is there an union in your organization?
Is there a risk of race, caste, religion, sex, language discrimination while pushing the employee out?
What is the level of the superior?
What was the topic of discussion?
Is the history of the employee suggestes similar behaviour?
Why urgency?
What if the employee continues to work for the organization?
Is there a clause in the order or appointment letter pertaining to removal of service with lesser notice?
Is the employee not interested to work for your organization?
Is the employment by nature, is stressful?
Was an enquiry been conducted? If so, what are the findings?
without answering these questions, throwing an employee could be difficult for an HR Personnel.
However, if you feel, employee should be out, and if you are small organization without union or labour problems, and if you are not a manufacturing unit, you can very well give one month salary to relieve him. This is highly riskier, if you do not answer few of the vital questions listed above. Personally, I do not subscribe the view of terminating an employee just because few smirkish activities been noticed.
As a good HR person, if your organization does not want to employ a person, talk to him and explain the issues behind the continuance of employment and take a resignation letter from him.