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

This never happened to me. I must’ve had a terrifying LOOK!!!

In the old days 1975 - 1980 take the soldier behind the old barn and the soldier walks out. end of discussion.

As an E5 in the 82nd ABN ,I'd smoke his ass first,then leave him in the leaning rest until he ETSed !

Written Warning 1st time with his/her Squadler present counseling session. 2nd time disciplinary action under UCMJ maximum punitive actions allowed.
Two, NOT three strikes YOU'RE OUT!
Note: Investigate climate in your unit for UCMJ support.
Why? Because the Armed Forces UCMJ may have shifted due to Woke influence!

Article 15,

"Half right, face! Front leaning rest position, MOVE!"
"In cadence, exercise!"
"One, two, three, one, two, three..." Repeat until they do 100 solid pushups.

Respect is earned and if you have that this will happen rarely. That being said, disobedience or disrespect must be dealt with immediately. Forcing the man to do the job will only result in a job poorly done however privileges can be withheld and will demonstrate both your leadership and authority.
BUT I'm from the brown shoe army and things were a bit different back then.

Simple UCMJ their ass and let the paperwork do the working for you.

If the private was dissatisfied with his assignment and mouthed off, I would immediately (and in the presence of the formation) change it - to something infinitely worse, the dirtiest, smelliest, most onerous and exhausting task there was. If there wasn't one, I'd MAKE one. I'd let him know that this was going to be his lot in life for as long as it took for him to get it through his thick skull that he would do what he was told to do without complaint. If he balked at it, I'd bring him up on charges and see how he liked that.

How about standing in a front leaning position until I was tired