The university, located in Halifax, Nova Scotia, said two student organizers face disciplinary action over the incident, in which students chanted their desire for non-consensual sex with underage girls, the Canadian Broadcasting Corp. reported.
The episode occurred during a freshmen orientation week event.
"It is with deep reflection that I tender my resignation," students association President Jared Perry said in a release Friday evening. "I believe this action is in the best interests of the students, the association and the university."
Perry said he would work to fix the "damage earlier this week to the reputation of the association and Saint Mary's University."
University spokesman Steve Proctor said a formal complaint had been received Friday alleging violations of the Student Code of Conduct "for the use of abusive or offensive language or gestures at university sponsored functions." He said a disciplinary hearing would be held within 10 days, with the unidentified students facing fines, suspension or expulsion if the violations are substantiated.
Carrigan Desjardins, who was responsible for the freshmen's week program, resigned as vice president for student life.
Saint Mary's administrators have apologized for the incident, which was recorded on video that was posted on the Internet.
The video shows students chanting, "Y is for your sister, O is for oh so tight, U is for underage, N is for no consent, G is for grab that ass, SMU boys we like them young."
University President Colin Dodds said he was sorry "students, and now the community at large, were exposed to disturbing sexually charged material," QMI Agency reported Thursday.
The 80 student leaders involved in the video will have to take a sensitivity seminar by the end of month, Dodds said, and the head of the student association is being required to attend a conference on consent and sexual assault.
Dodds added he would establish a council to determine how to prevent sexual assault and sexual harassment on campus.
The video was released during orientation week, during which student representatives oversee events. Proctor said the university might consider assuming more responsibility for the events, CBC News reported.