How to respond when insulted by a grad student in a different department?
I'd probably document it (make a dated note to yourself someplace noting what occurred and exactly what was said, while you still remember it) and then ignore it, unless it becomes a pattern. The purpose of documentation is to start a record in case the behavior turns into something more regular.
The exception I would make is if you have any reason to believe this student is abusive/insulting to anyone vulnerable or deserving more protection. For example, if the commentary is racist, sexist, homophobic, etc. If it's more of a "(expletive) you" I'd let it go.
Normally you can simply ignore such things. People like that mostly harm themselves and other students are unlikely to support them in their bad behavior. I was once publicly, but anonymously insulted and didn't respond. My students jumped in to explain to the miscreant why they were wrong. Problem solved.
However, you have a right to respect in the classroom. If they behave incorrectly you can ask them to leave, especially if it is disruptive. I think that you would get wide support for ending disruptions, both with the other students and with administration.
But, yes, as Bryan Krause says, document it.
Unless he is actively stalking you outside of classes, I would just ignore his comment on the campus. The problem will go away when he leaves college (either voluntarily or involuntarily), or when he grows up, whichever happens first.
On the other hand if his behaviour is unacceptable in your classes, you are in a position of authority and you need to maintain that authority for the benefit of all the students.
If he does it again, I would give him a public verbal reprimand, and remind him (and the rest of the class, of course) of what powers you have - I assume that includes the right to remove him from the lecture room either temporarily or permanently.
If he is bone-headed enough to escalate the situation, let nature take its course - evidently he didn't win his first battle, and the details of that will already be on the record somewhere.