probably should. He’s clearly not able to control his impulse to be a jerk. You can’t say “I hope you die” to someone and not have real consequences in your professional life. If one of my employees said that to someone and it became public, I’m sure I would fire that employee.
I’m not one of the ones calling for anything nor am I even involved in Twitter because I’m an adult. But we all have seen how social media works. You simply can’t say hateful things. You’re going to have it come back at you. Gotta be smarter than that.