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

This is an interesting question, and probably has about 100 correct answers,depending on the respondents.
Not that I a picking on our brethren in Air Force Blues, but I would think that an E5 in the Corps, would handle it just a little differently than the AF. I was an HT1, and I guess you could say a little old school, and was probably able to discipline a little different when I was in as opposed to now. But either way, or any branch, when an E5 is issuing orders, you do as he or she says, you say "Yes Sir/Maam, and you go on about your day.
This is what i truly loved about the military,they did not have to put up with all off this touchy feelty kind of crap, you just did what your were told, and if you did not like it, then after you completed what you were told, you went to the next up in your chain of command and voiced your concerns there..
Just my two cents.

make him an E1 to start with

Write him up

Article 15 for sure. There used to be a unit called CCF (?) correctional confinement facility I believe. Or something like that. Used to be able to send idiots to that for a couple weeks or so and they usually came back with a different attitude. Now I don't know what you can do but Art 15 them with reduction and eventually confinement.

At my first command, as a junior E-4, I was the LPO for 1st LT division. Whenever a new person checked into the Division, my LT would tell them straight up, any order I issued, they were to take it coming directly from him and they would be up on charges for disobeying a lawful order from an O-3, not an E-4. So, I never had a problem. But, I knew if I screwed up, My LT would hammer me also. Support from my chain of command was the biggest reason why no one questioned me. That was in the late 80's early 90's.

Their next assignment would be a relatively short discussion in my office followed by weeks of less desirable assignments. After that period was completed. I will have made an evaluation of their progress including keeping an ear to the ground about any bitching. I would of course hope that more senior members of his squad would have been kind enough to mentor the dumbshit. I'm sure I might have gotten opinions offered up and taken in from the more senior PO's reccomendations regarding the individuals future viability would certainly be added to their record if progress was unsatisfactory.. If they took instruction and improved their attitude my evaluation would be likewise tempered or simply given a satisfactory rating. Young soldiers especially in specialties which allow for quick promotion are still basically untested and yet to be properly indoctrinated in day to day military life. I will not take action to shit on them long term if improvement is acceptable to me.
People might wonder how someone who never made it past PO3 might make such assertions.. I have made 54 trips around the sun and learned professionalism and discipline in my own field.. At the end of the day it amounts to the same thing. My job is both dangerous and requires great responsibility.. I run 145,000 lb 93' long at up to 75mph on state and interstate highways 135,000 miles a year. I better keep my act together because Im in control of a 70 ton bomb..I am fully accountable to myself, God and everyone whose life I might affect every day.. Anything beyond that is just a good time working in an office with a view and a good paycheck.

simple write up and then a general court matrial but Im from the old school Army where respect was taught and no pampering was done

Remember the scene in "Full Metal Jacket" with the troop marching behind the formation with his pants down and thumb in mouth? Happened twice to the same mouthy EM in my basic training company in 1967, except the Drill Sargent didn't make him drop his drawers. Results? None. He thought it was funny. Spent most of his time on KP, he thought that was funny too.

Make an example of him. civilians may allow that behavior, but that E2 is in the military now. In the heat of battle a machine gunner goes down and to tell the E2 to get on the machine gun the response will be get someone else.

If you find yourself arguing with an E-2 you need remedial leadership training. You are molding character, the clay is in your hands. Discipline must be swift, decisive and carry the message that you are not paid to argue with pvts. Make an example but not a spectacle. If you are able to, try to consider the indiv. and teach him a lesson without ruining his career, you may have a good soldier who just needs to get guidence. But you need to have control of your people
Best of luck