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

Death by skull fuck.

That E-2 must be a liberal that signed up for the wrong trade.

Well I'd probably laugh at them and make them feel really small and order them to do it anyway!

HAVE HIM LOCKED UP

well I am not in the military.but I do think that when you are in the military there are rules inplace that help you and that you are there to learn that can and will save you and your men.so yes he needed help to see why he should to as told.

I would have needed a new pair of boots!

I had this happen to me plenty of times. I was an E6 and had NO support form my command. I decided to stay the course and take the high road. After the senior command moved on/ retired I was the one in command. I did such fun things as write counselling statements and confiscated cell phones. I had to make all of the subordinates to Unlearn everything and get them on the right course. As I retired I left behind a great maintenance section who as a group excelled. I say nip it in the bud. If it's an ongoing thing, talk to the private to find out what's going on but remind him that he is a soldier first.

Give everyone else in the platoon extra Duty, explain to them that they got the extra to Duty because off this man's insubordination. As the others complete their assignments have the dissenter stand in a place of prominence and watch them all. At the end of the day have them all report to the barracks and lock the door behind them. By next morning he should understand how things work.

In today's military, it is important to cover your butt. Witnesses to any form of correction due to insubordination is a must. Too often the benefit of the doubt is extended to the subordinate complainant and not extended to the NCO or Commanding Officer who are charged not just with unit cohesion but with the lives and well being of those who would file the complaint.
That being said, there could be an underlying cause to a sub-ordinates reticence to follow the lawful directives of an NCO or the lawful orders of an Officer.
Care should be taken to provide a witness to any further interaction with the sub-ordinate. Dismiss all but E2 and his squad leader. Question the sub-ordinate as to the reason he/she is unable to comply with a lawful directive of an NCO or the lawful orders of an officer. If there are not sufficient extenuating circumstances, then the E2 should be informed that not complying with the Directive or Order given will result in actions being taken against the E2 according to the UCMJ which will begin with MP's being called to assist in the detention of the offending E2. If there are extenuating circumstances that would justify an inability of the E2 to effectively comply with the Directive or Order, then it is important for the E2 to understand that proper respect must be shown and demonstrated at all times to the Chain of Command. Suggest to the E2 a response that would have demonstrated this respect, but have allowed the NCO or the Officer to directly address the concerns of the E2 without delay.
This of course is assuming that this is not happening in a combat situation. The immediate life and death nature of a combat situation will probably make all of this irrelevant to the immediate needs of the unit. Many factors could play into the E2's unwillingness or inability to comply. These factors may include but are not limited to combat fatigue, fear, intense shock and confusion, overwhelming grief from the loss of a unit member, anger at the failure of Command to sufficiently assess potential threats, etc. The immediacy of combat makes this situation much more difficult to easily address. Proper training helps to insure that this situation does not occur in combat through the confidence gained by instinctual application of that training. Encouraging the E2 by expressing that they have been trained specifically to deal with combat situations, by stressing the needs of the unit as a whole and that lives depend on their ability to carry out Directives and Orders, and by the E5 expressing his/her personal confidence in the E2's ability to perform the given task successfully will probably produce better results than threatening the E2 who may in turn become more entrenched in their position to not comply with orders which not only results in a breakdown of discipline but of unit cohesion and combat effectiveness.
It is important for the E5 to remember that the United States of America has invested much time, effort, resources, and tax dollars in developing this E2 for service in our Armed Forces, and that motivating E2 to perform effectively their assigned task protects the investment in this individual that the entire nation has contributed to.

Dog his ass, if still not compliant, counseling, not compliant still, move to article 15.