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

Finish up the briefing, dismiss everyone else to their tasks and then correct the E2. After the correction, send them to complete the assignment

Shitbird would be on every nasty cleaning detail in my command, plus his original Lawful order assignment. If he mouths further or slacks off he'd get additional lawful assignments that would etract from as much sleep time as allowed. After that the Brigg followed with circular file of his career.

Give work assignment to the most influential squad member that didn't have an assignment. He will take care of his peer. Make a note of the situation. When PVT SB's
up for promotion kick him out under AR 635-200, General But Honorable Discharge.
Did this 100 times in my career.

Re-assign the duty to another squad member.
Make note of the situation.
When PVT SB's up for promotion to E3 give copies of your notes to Platoon SGT.

Lol....There are several ways to handle this situation, I'm going to assume this the new generation of Soldiers. Once I release everyone that Soldier will standfast, it's obvious this Soldier is going through something and it's my job as a leader to find out. Once the issue is identified and some type of resolution is given. Then I would have a conversation with the Soldier anotating everything on a DA Form 4856 explaining where he/she went wrong and the consequences of his wrong doing. Once the dust clear he/she would no longer be a fresh E2 with less than a year in, he/she would be a newly demoted E1 with less than a year in.

In the old days he would be picking himself up off the deck but this is the kindler, gentler military.
Before you beat me up for that view Google Chinese/Russian military training

Possible Article 15 or counseling session, advising them that such behavior is not tolearted in the civilian sector either.

There was a time when there was no question as to what to do.

E2 smart mouthing? He'd be an E1 really fast

Wow!! I would write them up (counsel them) for disrespecting an NCO and disobeying orders and give them correctional duties that would take away much of their time and that are physically taxing. For example, before PT (around 5:30 a.m.) they would have to report to duty in ACUs and perform police call around the battalion or battery/company area and when they were finished they would have to change into PTs and still do PT. Before they go home in the evening, they would have to clean up some kind of cleaning details. If after all that or during that, they were still disrespectful then it’s time to start recommending for punishment