Around 1,208 students voted in favour of Bose's resignation while only 316 students said he could continue holding the post.
The university's student body, Independent Consolidation, organised voting on the issue for two days in which a large majority of students participated. The result was announced today.
The result will not be binding on the authorities as it only reflects the choice of the students.
They will soon meet Sugata Bose, who is the Trinamool Congress candidate in the Lok Sabha election from Jadavpur constituency, and convey him their decision.
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"If he doesn't step down we will continue to protest against him," the students' union leader said.
Bose, who is also a Gardiner Professor of Oceanic History and Affairs at Harvard University, has already hinted that he wants to continue with the post.
During the voting, students were asked to cast their votes as "Yes" or "No" on the subject.
The mentor group was set up by West Bengal Chief Minister Mamata Banerjee to provide recommendations and a roadmap to turn Presidency University into a pre-eminent institution of learning of international repute.
Nobel laureate professor Amartya Sen is acting as an advisor to the group.