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

Bad in the days..... never mind

I had a similar situation happen to me when I was a Drill Sergeant. First thing is do not allow your Soldiers to loose it over this as this is what the PVT wants you to do. Next is it must be handled immediately and I recommend telling the PVT's Team Leader and him stand fast while everyone else falls out. Once it is only the PVT, his Team Leader and you explain to the PVT in very clear forceful (try not to yell) language what his options are
1. Execute the orders given to him in a timely manner to standard.
Or
2. Explain you will write a counseling statement recommending him for disrespect to a Non-Commissioned Officer, failure to follow an order and even insubordination.
If the PVT chooses 1 then do some research find out what the problem is and have a talk with him about how lucky he is and he won't be lucky a second time. If he chooses 2 then go to your Playoon Sergeant find out his recommendation (for me it would be UCMJ) and then execute the counseling and corrective training.

Walk the troop away from his peers, but keep him in view. Allow the kid to explain his actions to you out of earshot of the others. If, like a few of the others have suggested, and there is an emotional reason show compassion for the troop and offer the correct assistance. If the kid is just being a "Millennial", smoke his ass in view of his peers!

He & his immediate supervisor would stay, as I send the rest their assignments. Then I'd ORDER Him to obey my Lawful Order.
The ARMY/MARINES are NOT a Democracy.
You signed up for it, Idiot!!
Do we have to provide "Safe Havens" for them in Combat??

Hit the deck.

Failure to obey a direct command bring him up on charges

Well i would pull him off to the side away from everyone, and ask him what is malfunction was? There could be something serious bothering him. If you find he has nothing bothering him then it punishment time! If there is something bothering him, lets see if we can help. He must know that no matter what his insubordination will not be tolerated!

Take him/her up the chain and get them the discharge they want.

I use the old fan room counseling bit. I was Navy and think the old school ways need to be brought back.

there is not enough information here to be useful. We need to know if there is any other issues prior to this particular scenario. The real answer is there are many ways for the NCO to react and show his leadership to the others present.