The Council may remove the Mayor for gross misconduct, or malfeasance, misfeasance or nonfeasance in or disqualification for office, or for the conviction while in office of a crime involving turpitude, or for a violation of his oath of office; provided, however, that such removal shall not take place without the affirmative vote of two-thirds of the members of Council nor until the Mayor shall have been notified in writing of the charge against him at least ten days in advance of a public hearing upon such charge, and he or his counsel has been given an opportunity at such hearing to be heard, present evidence, or examine any witness appearing in support of the charge.