As a recovering "class clown,” I used to think that contributing sarcastic or witty comments to a meeting helped ease tensions or relieve boredom. Some folks agreed with me. But a coach I hired 20 years ago helped me see that my behavior would be experienced by many as: insubordinate, disrespectful, unhelpful, controlling,.... Well, you get the picture.
I can honestly say that up to the point of my coach's intervention, I had not considered the unflattering ways some of my teammates might experience my "humor." Since then, I am much better at governing what I say aloud.
It is possible that your bright subordinate doesn't know the negative impact he's having. It’s also possible he knows and doesn't care, perhaps feeling he's too capable to be demoted or fired. If this second story is the case, you probably need to take formal corrective action complete with clear guidelines on expected conduct and consequences if he fails to change.
My bet is that he is unaware of the impact he's having, and would be chagrinned to find out. With this in mind, I'd have a 1:1 conversation where I would play back some of his verbatim comments and ask what he intended. He would likely defend his words, or indicate a benign intent, and I would then offer him some alternative interpretations. I might mention that other team members have quietly complained about his style. Hopefully, he will feel mortified and indicate a desire to change. If so, I would propose a plan where he works on his behaviors and word choices, and I offer to provide him rapid feedback.
If the 1:1 approach doesn't work, then I might start "correcting" him publicly in meetings. For example, when he drops one of his sarcasm grenades I might say, "I don't know about others, but I am negatively triggered by your choice of words and tone. If you have something constructive to add, I'm eager to hear it. But please don't waste our time with unhelpful comments."