Can a corporal in a team leader position have me do corrective action (“smoke” me)? And was I wrong to tell him to eat a bag of dicks?

You shouldn’t be in the military if you have to ask that question.

Under the Army's SHARP program, you exposed yourself to additional problems by your particular verbal response.

This is, of course, over and above, the problems you could have faced under UCMJ.

Plain and simple, He was in a leadership position, in your chain of command, so the answer is YES!
He would be within his right to refer you for UCMJ action.

Good for You

I was a CPL for what seemed to be an eternity. BLUF, in my opinion it's probably the hardest rank in the Army to navigate. A SPC doesn't want to listen because they are the same pay grade (NOT RANK), and seniors only treat you like an NCO when they have a detail they don't want to handle themselves. That said, if you have been doing the job long enough to know that the CPL was wrong you should have pulled him to the side and had that conversation. The CPL was most likely embarrassed because you called him out in front of others. Think on this, if I as a MSG or as a 1SG, call out my CSM and he barks at me, then I say CSM go eat a bag of ----! How do you think that will turn out? So when I disagree with the CSM, I ask to speak with him and we have a conversation. No one gets chewed up or embarrassed and we figure out a solution. It's all about approach and delivery.

Back in my day you could still go behind the wood shed in a case like that. After Nam had a Sp5 Motor Pool liked to yell at the Troops, did it to one of my guys. When I found out I told him if he had a problem with one of my guys, see me. Well he did it again and learned I was not fooling, his name happened to be Chuck Norris, not thee Chuck Norris. It was early 70's, the guys would always tell any new guys, watch out for the Sarge, he whooped Chuck Norris's butt. It was fun cause I was only about 155 lbs back then, the newbee's would be real good, we all chuckled when they finally met Sp5 Chuck Norris at the Motor Pool

I have to agree with everyone. You could've handled it more professionally. I hope this was a wake-up call or a lesson for you. If you were in 20 years ago, you would've gotten more than corrective training. You have a squad leader and a platoon sergeant for a reason. You do have the right to speak to them about any issues that are going on within the platoon. I know every new generation of service members is different, but you can't disrespect your superior. Trust me, if you had done that in the civilian world, you would've been fired in a heartbeat.

Disrespect to a NonCommissioned Officer, Insubordination, new Army mind set about leadership. Why is this even a question. Wrong is Wrong put yourself in his shoes. This is totally unacceptable, hopefully the Squad will get wind of this and give you some real corrective actions.

Yes he or she can. And in the interest of diversity, you may want to, in the future, mix up your unprofessional and disrespectful remarks by saying, "Eat a bag of cunt$", or "eat a bag of they/them/theirs". In the end, you have been disrespectful of the authority, regardless of the rank. Shame on you.

It all depends on the reputation, who knows who and who knows what. Now in the infantry world, this is a no no. In other more technical fields depends. If you are the senior specialist in a field that is super hard to promote in, and you just got in a recently reclassed NCO, or that NCO is a known idiot, you might get away with it. I have, but this guy nearly killed people due to his idiocy. He tried to pull rank, I mouthed off, called out safety, SOPs, and basic practices so we don't kill people in training environments due to monumental stupidity. But I gambled on reputation vs reputation, but I joined as an older person, and grew up and served in an environment where sometimes expertise, experience and scope of practice out matches rank.