How would you react to an E2 who "smart mouths" you in formation?

I can only speak from my time error when things were very different, so here goes. First off, the E2 wouldn't have come to you with this problem. They would have had it dealt with long ago. There were ways, back then, that you used to, lets say, persuaded someone to fall in line. Sometimes it took a little more persuasion then others but believe me, they did fall in line.
I understand in today's military, things have gotten soft. You can't reprimand other then vocal or putting them on report, there is no inbetween. I think it's an injustice to the recruits because they will never experience or have the opportunity to first hand feel the discipline that was or is the United States Armed Forces. That in itself is worth it's weight in gold. That is what the military was built on, chain of command and following orders. and understanding the UCMJ , because if you dont follow orders, people die and that's not acceptable.
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Say be quiet Pvt. One more word out of you and you are going to see the company commander and see what he has to say about your smart mouth

how you present your self as an nco determines how those kind of things play out! not one of my men would dare tell me something like that! first off I am old school, I have been known to go behind the barracks and instruct a young one on proper protocol between ncos and those below them! but I also stood up for my troops daily! I would say the team leader and I would have taken that young man out back and team leader would witness me schooling him!

I think there is a touch of an officer and a gentleman in this survey. WE THE PEOPLE exceed even the supreme court

courts martial. immediate and sets the stage for the next pos. to obey the chain of comand

I'd have a calm one-way discussion with him or her about how everyone has to do things they don't like and the importance of working as a team. Perhaps add a clear reminder of the meaning of respect and how it is a two way street. Moreover, if he or she has a problem with it, we can always add other less desirable tasks to his or her plate. End of discussion.

All good responses. I would make him apologize to both you and the in front of the formation (I did that once), write up a counselling report and give it to the Company 1SG. The reason you give it to the Top is, maybe the next time he smarts off at someone, it's someone else and not you, and you might not know it. So thee has to be a record. As you counsel him, if he opens his mouth or shows any attitude at all, he's a prime candidate for an Art 15 (this time around.) The 1SG will assist in handling that - with the commander. Next time, it gets even tougher.

Oh man. I'm a little old school. Ok a lot old school. First I'd start off with a good old school smoking, then I'd find every that young soldier every shit detail I could find. He'd either soldier up or take a bus home. I'm happy to be retired, because there's no way I could or would kiss a young soldiers ass. I remember being smoked and I promise I never made that mistake again. Quit babying these young punks or they'll tell you in combat not me Sergeant. Teach them now.

Oh man. Please know I'm a little old school. Ok a lot old school. First I'd start off with an old school smoking. Then I'd find every shit detail for this young soldier. He'd either soldier up or take a bus home. I'm not a big fan of todays military. I'm happy to be retired, because I couldn't kiss a young soldiers ass. Punish him and punish him hard. I remember being smoked and I promise I didn't make that mistake twice. You don't teach them now, they'll always be shitbags.

Depends on the situation but I would likely act as if I did not hear his/her smart remarks until after I dismissed the formation: And I would ask the E2 to stay back so I could have "a word with him/her"
(This goes without saying, as a male, if this E2 is a female, I would also have another NCO of the same gender accompany me...a little briefing to the associate NCO would be in order, as well.)
I would explain how the service works and advise that their attitude needs to get in alignment with the needs of my branch of service. Then after I "delicately" explained how this behavior (that they displayed) was not acceptable, I would make it CLEAR, in no uncertain terms, that if that EVER happened again, I would file the appropriate paperwork that would follow them through-out their career, or I would ensure their career came to an abrupt end. Then I would give this E2 a chance to respond that they completely understand exactly what I am saying. I would also make it CLEAR that they are never to demean or "sass" me, or any superior, EVER again in public; formation, off duty or otherwise.
The military requires trust and respect and one cannot take place without the other.
Now "get on-board or get out."