I don’t know the specifics of how everything works, but I could see a path where he could do that, legality of his actions notwithstanding.

My guess is that international students applying for student visas need to list what university they’re going to attend. I could see Trump ordering that the State Department simply decline any visas for students that are heading to Harvard. That would essentially accomplish Trump’s goals and leave Harvard in a position where they can’t really do much about it.