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

Just do it. There's a whole lot of suck in the military. But being the guy/girl who embraces the suck, gets a lot of respect from the majority. That person would do anything for the team. And does it because if they don't, someone else will.

If you can't take a direct order you can potentiality be a liability .

Discipline will be required after you dismiss the others....add some extra military instruction and document ALL of the events.

First off, handing out work assignments is done between squad/platoon leader. If the squad/platoon leader has a problem with a soldier then he brings the problem to you. But if the E-2 has been in service for six months this situation would have been corrected before this incident presented itself. To be in six months and still showing this behavior shows prior training was defective and needed to be corrected and isn't the soldiers fault. Get his squad leader to proceed with the assigned task and get this E-2 to stand by. In private one on one explain to him that service was voluntary and if its not for him then process him out. If he wishes to remain part of the group then his compliance to your orders must be followed to the T and without question. He must understand that someone else's life depends on this and anything less than his total obedience determines their life's continuance. Allowing him to be in control of the situation undermines your authority and cause others to doubt your leadership. But creating fear to the rest of the squad/platoon is not a motivation to perform or performance in a combat situation. Many an Army lost battles fearing their leaders as much as their enemy. Genghis Kahn would take over a village, but would feed and take care of the villagers to get them to join. Thus service to him was voluntary and his army committed.

Smoke session until their eyes bleed

This is an art. 15 if I am not mistaken , I'd tell him to get into the head and deal with him there when he returned to the formation the answer would be clear and no witnesses

The swift hand of Authority. PT him till he remembers that his ONLY response is Yes Sargent.

Why the hell does a Drill Sergeant have his sleeves rolled up?!? Must not be a disciplined Infantryman (we wouldnt dare roll our sleeves up unless we were serving food in the field)

Clear the room

Beat your face. Push until my arms get tired.