"I believe it is the right course of action for the Mount at this time," he said in a statement, according to The Times.
Newman's resignation is an about-face from his position a few weeks ago.
In February, professors called for Newman to step down in an 87-to-3 vote, but he declined to resign and played down the importance of the vote by saying professors voted "as a bloc."
Newman has been the focus of negative attention since the Mountain Echo, the student-run newspaper, interviewed two faculty members who said the president had referred to struggling students using a bizarre analogy during a meeting with faculty members.
"This is hard for you because you think of the students as cuddly bunnies, but you can't," Newman was reported as saying in The Echo.
"You just have to drown the bunnies … put a Glock to their heads," he continued, two faculty members who attended the meeting told the student newspaper.
Newman previously told The Washington Post he didn't remember exactly what he said in the quoted conversation but acknowledged that he sometimes uses language he regretted.
The student newspaper also ran an unflattering email exchange between Newman and Provost David Rehm in January, in which Newman proposed a plan to encourage struggling students to drop out early in the year.
Newman has received particular criticism for what might seem like an attempt to silence student reporters.
One fired faculty member, Edward Egan, advised the student newspaper that leaked the email in which Newman proposed encouraging poor performers to drop out early.
The move would improve the retention rate, a metric colleges care about because it affects their ranking on lists such as the US News & World Report.
Thane Naberhaus, a professor of philosophy with tenure, was also fired recently. His dismissal notice accused him of disloyalty, according to Insider Higher Ed.
The school eventually reversed course and reinstated two of the professors, Inside Higher Ed reported.
MSMU and Newman did not immediately respond to a request for comment.