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

is this in the Corps or the Navy? Either way, seems to be an issue through out all services. Soldiers or marines are not being broke down and build back up as they use to. So approach is totally different from 10+ years ago. Discussion can begin with "At ease", then "Stand by after formation", conduct one on one counseling verbally. (Your career can depend on it, depending on how your chain of command is)
At the same time, by experience most soldiers will do as they see (like kids with their parents) If they see NCOs or Officers do the same as example, why they cant do the same?. This is where you step in as an NCO and explain about Discipline and provide leadership instead of just barking. What kind of climate/environment is this?

"The pen is mightery than the sword!"

I would take immediate corrective action in front of that same formation. You cannot allow toxic behavior to usurp your authority in front of your command structure. The effect can be devastating on unit discipline. Military bearing and professionalism are the foundation on which duty and mission performance are built.

Right to the orderly room, ask why they refused your order. Have a witness. Them smoke them all day.

A Letter of Repremand would be appropriate.

Assign the task to someone else, counsel the soldier after formation and then report the incident immediately to the platoon sergeant or if you are the platoon sergeant, to the first sergeant.

The NCO chain will then do its job either by identifying the soldier's problem (who knows what he is going through), and either informally or formally punishing as appropriate.

As a company commander I had a soldier who started mouthing off to his squad leader and platoon sergeant. The first sergeant and I talked about it a few times, and after learning that the soldier's brother had just committed suicide, we got that soldier help instead of an article 15.

Take them around the corner of the building after formation and perform corrective training. Don't put it on paper unless you need to and don't call them out in public.

When I was in basic at Ft. Lewis in '73, I made a smartass remark that was overheard by my Drill Sargeant while we were in the field. 50 push-ups with a PRC-77 and an M60 on my back was the first phase. Then I humped those two pieces of equipment, along with my M16 and basic gear for the next 72 hours. Upon returning from the field, I had latrine duty for two weeks. It was amazing how my attitude changed, I was told.

Permanent shitty details until they accept one without complaint.

Well first I have to say, I was always the Soldier to disagree with Madan task. Never in front of other soldiers but off to the side. I was very fortunate to have a squad leader who understood my disagreement. I never questioned a direct order. But we have all had the daily task of BS. I never tried to get out of doing work but if I could make it easier to complete the task with less men ,so others could have down time I did.
So when I became a Sgt. No one questioned me because they knew I had already broken down the task and what was left had to be done. I believe if I ever had a solider disrespect me my other soldiers would have had a little talk with them.