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

As a 1SGT I would have the leadership team stand fast a d follow me to the office. I would invite the Plt Leader to attend. I would ask if this is an ongoing problem or does this soldier need special attention. Insist on a written plan for the Pvt. then I would have a little talk to the NCO,s about my expectation on there leadership style.

Where has our military gone for some young shit bird to even think he can say such things and it’s okay? Next stop would be, Section Commander, with shit bird, his supervisor and me. Shit bird would receive a position on the “goon squad” until his discharge was official. No excuse for this type of disrespect. If shit bird can’t follow orders, then he is a detriment to his uniform, especially during a war time. Time to thin the herd before the shit hits the fan in real life.

These comments are funny
The only thing that needs to happen is a swift knife hand spittle in the face and instant physical destruction

Remove him from the formation to an office scenario setting and let him know hos the "Bear reacts in the woods". Once then he is headed for "Office Hours" for insubordination. Give me a break, the tail wagging the dog will not make a winning team.

pushups a lot

The "School of The Soldier" was normally effective especially while everyone else was on pass. The 1SG and the CSM could also be quite inventive where the objective was to get an errant soldier's attention, versus formal charges.

Busted in rank, brig time, one way ticket home, and a record that will follow him even after he dies!

PVT A$$hole has just stood up to an E5. That takes a certain amount of courage (or insanity...but let's be generous here). Something like that might have value if it is correctly managed and aimed. Clearly, aiming it at the E5 in the chain is not good.

So, let's see about managing it and getting it vectored into something the Service can use.
Step One: Completely agree with dismissing all except PVT A$$hole and Squad Leader, thereof.
Step Two: Completely agree with conversation as mentioned (see discussion above, thanks to GySgt Kenneth Pepper).
Step Three: Remind PVT A$$hole that his Unit, and Leadership, thereof, are NOT his enemy. We all want PVT A$$hole to succeed. PVT A$$hole does seem to have some balls, and we would like to see them used against the ENEMY, not his own unit.
Step Four: PVT A$$hole gets to chose. Get his rear en moving, as directed, or see thedoor.

Yikes! Disobey a lawful order, malingering and insubordination! Pretty serious stuff. Article 15.

I’m an old Vietnam Combat Infantry Recon Rat. Got my training and experience before the Army became “Pussified”. Everyone looking to “correct” someone else for stupid shit. A little “behind the barracks” education worked every time stateside. In Nam, you could experience very severe consequences for that kind of response. In general, yakking back at an NCO was a VERY bad idea. If the NCO was the recognized asshole, he could be scheduling himself a blanket party. Things were taken care of in-unit, stateside or in theater. But this was a tip-of-the-spear combat unit. Don’t comply, you (or we) could die. If you were told to burn the shit pits, or crawl into a suspected VC village, both commands held equal weight. It wasn’t a “Job”, we were all part of a well-trained, well-oiled military machine. Sent to recon, observe and report, kill only when necessary. Captured VC, or even village chiefs, were intelligence troves. it was done quietly and efficiently. Sent to contact and neutralize, it was done with the same efficiency. THAT was the job. And we were excellent at it. The military is designed to kill people and blow shit up, better than the other guy.
Disobeying a direct order to, for example, adjust or use a drone attack in today’s Army could be just as fatal to a team like mine (or worse) as hesitating to take out an enemy up close and personal.

Rank needs respect; obedience needs priority in today’s Army. It’s a JOB okay, but with extraordinary requirements and commitment!