How do you handle a strong engineer whose behavior is damaging the team?

Address it directly and early, and treat behavior as part of performance rather than a separate soft issue. Give specific examples of impact instead of character judgments, and be clear that output does not exempt anybody from the standard. Set observable expectations with a timeline, follow up, and be genuinely prepared to lose them, because tolerating it costs you the people around them.

I move quickly, because the cost is not the incident itself, it is what everybody else learns about what gets tolerated. I keep the feedback on specific observable things: in yesterday's design review you cut off a colleague twice and called their proposal naive, and here is what happened next, three people stopped contributing for the rest of the session. That is much harder to argue with than telling somebody they are abrasive. I also say the quiet part directly: your technical work is excellent and it does not buy an exemption from how we treat each other here. Then observable expectations and real follow up, usually weekly for a while, with recognition when it improves, because people do change and pretending they cannot is its own failure. I have had one case that was genuinely fixed after a rough month, and one that was not, and we exited them. Losing the output hurt for a quarter. Two people who had quietly started job hunting stayed.