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

PRETTY DAM EASY ! As an E5 to an e2/3, wack him up side the head or UCMJ the smart mouth for disrespect & in subordination. If you give the person that just means some one else has to 'supervise' him.

Give him the day off give all his buddies double duty

tell them to lock it up their at the position of attention. then take him or her of the side with another NCO and have them explain themselves. Sometimes an Art 15 or personal counseling will fit. Explain to them there is a right way and a wrong way to say things in the Army but commands can never be left open for the individual to follow.

From my humble view, and I got out in 1993, I had the same thing happen while deployed; A PVT said "no I will not do it". I asked him again and explained that although it is no ones favourite detail, that this is mission essential and I only choose those who I know will get the job done". He stood his ground and balled his fists and clenched his teeth. I made the statement that he needs to go cool down and we speak later.
Later in a one on one he simply said he is tired of being in the desert and he is sick of being the private, he could not see the importance of this task for the mission. I let him go with a warning, counselled him and said that setting the example goes both ways; up and down, that he is a good soldier and I too am ready to go home so lets let it go.
the CSM heard all this and told me I did the right thing but at the next smallest detail, I need to lean on him hard.
That night I made the rounds to check the guards on the perimeter, I looked at who was missing and it was the same PVT, fast asleep in his fart sack...needless to say he got an Article 15 the very next day. If a soldier is a bad apple, he will remain a bad apple and the time will come where discipline is inevitable.
The real point here is your authority; did you keep control of the situation no matter what, were you calm and not emotional and did you end the discussion or did he. These points matter when other troops are watching. Remember: People follow leaders they respect, they dont follow anyone out of respect for the rank.
Good luck.

Discipline

From my humble view, and I got out in 1993, I had the same thing happen while deployed; A PVT said "no I will not do it". I asked him again and explained that although it is no ones favourite detail, that this is mission essential and I only choose those who I know will get the job done". He stood his ground and balled his fists and clenched his teeth. I made the statement that he needs to go cool down and we speak later.
Later in a one on one he simply said he is tired of being in the desert and he is sick of being the private, he could not see the importance of this task for the mission. I let him go with a warning, counselled him and said that setting the example goes both ways; up and down, that he is a good soldier and I too am ready to go home so lets let it go.
the CSM heard all this and told me I did the right thing but at the next smallest detail, I need to lean on him hard.
That night I made the rounds to check the guards on the perimeter, I looked at who was missing and it was the same PVT, fast asleep in his fart sack...needless to say he got an Article 15 the very next day. If a soldier is a bad apple, he will remain a bad apple and the time will come where discipline is inevitable.
The real point here is your authority; did you keep control of the situation no matter what, were you calm and not emotional and did you end the discussion or did he. These points matter when other troops are watching. Remember: People follow leaders they respect, they dont follow anyone out of respect for the rank.
Good luck.

I was an E2, you don't do it! I was in the 82nd back in mid 80's. I saw the decline of respect then.

Discpline

Heart punch

The value of respect has to be instilled in all who serve. No wavering at all. Respect the rank at minimum.

Put a huge coat of smoke on his fng ass

Straight blast him out of his boots. You don't ever mouth off to your NCOIC or D.I.

Choke slam them

Throat punch

Time to freak the hell out on a monstrous ass chewing

Show him my two BRONZE STARS from Nam & ask him if he had any more dumb ass remarks???!!!

See me after formation... Smoke the dog shit out of him... If that dont help counseling statement, article 15 ect..

I am new to the armed forces, but technically an NCO of higher ranks has the command to make the choice on whether or not a smart lower rank person can be rude to him or not. I would never in my life talk like that to an NCO that was in charge of me or my squadron. For one, it is disrespectful and could cause more harm than good when it is brought up to higher NCOs, you will be on their watch and they will see to it, you are their first priority to be taken care of and told of your orders on whether there will be punishment or you will be relieved of all orders and sent packing.

Tell that yard birds and squad leader to stand fast, dismiss all others to their assigned duties.
After all have vacated either contact the top or have the squad leader hold your stripes. With no rank involved conclude the business of insubordination. If that does not finish it then it is time to go up the chain of command.

Let him/her know that it is a one way conversation and responses/opinions are not necessary. Then pull them aside afterwards and get down to the nuts and bolts of why they decided to put their two cents in. If there are underlying (off duty or outside) issues then hangle it accordingly. But if it is just insubordination then lay the smack down. Counseling is a must with some sort of paperwork to annotate a possible turd in the work center. But definitely say something tactfully and professionally to the individual in front of their peers to let everyone see that it won't be tolerated and you won't be punked like that by a lower ranking individual. Besides I got more time in the chow hall bathroom than they have in the military.