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

First, Seek To Understand what he's really saying, Then Be Understood"(Stephen R. Covey -7 Habits Of Highly Successful People). This enables you to really understand what's going on, was he bullied or raped, are you mismanaging resources. Be a Principle -Centered Leader (Another Outstanding Stephen R. Covey best practice). "It's not my way or your way...it's what is the best way". Remember, Respect is Earned!

Write him up.

I would have him stand fast as the rest of the platoon is released to cover their duties.
When we were alone, I would give him the assignment again. If he accepts it or not, the next step is to the orderly room to discuss following orders, with the 1SG. Afterwards, discuss with the 1SG and CO about ART-15, extra duty etc. Make a believer out of him quick.

I have the FM for Wall-to-Wall counseling around here somewhere...

Wall to wall counseling and some extra duty with the team leader supervising should clear that up. Document it all and save it for the next time if there is one. UCMJ should be justified and the reasoning provable. Be sure you have a sworn statement from the team leader and a few others for good measure.

Better yet put him in a comfy chair and keep the formation at attention. Let him know in no uncertain terms he is letting his brother and sisters in arms down. His family their families etc. Put him on that assignment that he "doesn't like" until further notice till he learns humility. If he doesn't get out of that chair rapidly and snap to and do the job something tells me his peers will deal with him accordingly.

Offer him the option to be chaptered or comply explain it will ruin his life because his pansy ass probably talked to his own parents that let it go. Let them know your not mommy and daddy and your not gonna take his punk ass defiance. Give him an offer he can't refuse flipping burgers or serving out what he said he would do when he signed. If this kid has no honor let him know in no uncertain terms he isn't wanted amongst real soldiers. Hand him a Mcdonalds, burger king and KFC application and tell him to choose.

say nata until after formation then get them to the side and explain, that stuff will not be tolerated and please don't do that again if it happens again your looking at least at ar/t 15 at best, and then get after making the world a better place

This one's on me. You get one chance, and you've used it. Everything from here on will be official and permanent. Wanna lose any chance of ever advancing? Do it again.

Drop and give me 50