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

Violence is not the way... this coming from the main question and the comments. Back in the 1900 people people probably didn't fight back or he was out numbered but I guarantee that made him no better of a person/leader than kicking him out would have words are extremely powerful maybe slick sleeve lashed out on bad leadership/hazing. True he picked the wrong way to go about it. Wall to wall counseling or woodline institutionalizations don't respect the person either

I had a situation as an E6 where an E4 did this. I assigned the work to someone else then asked him what was going on. He told me I wasn't his boss and to f$co myself
Yes minutes later I get "invited" to see the CO.
Yep did that E4 is claiming racial discrimination. I get asked how I determined who to put on the detail. I told them I looked for the first 4 people I out ranked. The other three were not the same race as E4 did that. CO art 15d him.

Find out in private wtf? If it is attitude help him understand what he just chose for himself

As an O5, my first thought is that I'd turn him into an E-none. I appreciate that he might be undergoing some issue that caused him to snap, but it doesn't excuse his actions and must be corrected on the spot.

Ask them if they would like to tell that to the CO. They enlisted not forced as some were back in my day. When I joined all Marines were volunteers so that meant you did every duty assigned by some one senior to you. even time in the Corps not just rank. You remind them of that and let them decide how it is going to be handled.

That's easy...I'd tear him a new ASS in formation on-the-spot! He can try that "time-out stress card" if he wants to but I guarantee he won't be in the military much longer when I finish UCMJ actions!

I never have nor never will let that happen! HOOAH!

Remain calm; don't let your emotional reaction get the best of you. Instruct the Squad Leader to fall out of formation with the offender and bring him to you. Have a quiet conversation with the private about proper military discipline and respect for the chain of command. Ask him if he understands. Then instruct the Squad Leader to drop the private for 50 pushups and return him to the formation.
If the problem persists, it's time for Article 15 punishment.

Lock them up at "Parade rest". Get the rest of the detail out to their assigned duties. Get the PSG on the horn ASAP. Nature will take its course from there. Either "Joe" will have an epiphany moment or will be laying the groundwork for a pretty straight forward company grade conversation w/the CO & 1SG

how about stop being a bitch and choose someone else

I'd shine my boots with his ass.

This is, in no uncertain terms, insubordination. Definitions and possible penalties spelled out in UCMJ, Article 91. So...I'm right in line with Gunny Pepper (below).