Can a university suspend a student even when he has left university? If a student is supposed to be punished with something like suspension, but he has finished academic requirement and left the campus(not officially graduated yet). Can the university still do anything to him?
Yes. The university can revoke the degree. Example, which was about a PhD degree being revoked because the student later went on to commit academic fraud.

If the student hasn't graduated then the university can also withhold graduation, which as far as I know is quite common. For example if the student has outstanding library loans, the university can withhold graduation until the loans are settled.