The Council may remove the Mayor for his disqualification while in office, for his conviction while in office of a crime involving moral turpitude, or for a violation of his oath of office; provided, however, that such removal shall not take place without the concurrence of two- thirds (2/3) of the members elected to Council, nor until the Mayor shall have been notified in writing of the charge against him at least ten (10) days in advance of any hearing upon such charge and he and his counsel have been given an opportunity to be heard, present evidence, and examine any witness appearing in support of such charge.