The office of district superintendent of schools shall be vacant upon:

1. 1. The death of an incumbent.
2. 2. His removal from office by the commissioner of education.
3. 3. His filing in the offices of the commissioner of education and of the clerk of the board of cooperative educational services his written resignation.
4. 4. His acceptance of the office of supervisor, town clerk or trustee of a school district.
5. 5. His failure to take and file the oath of office as provided in this article.