Hey, I'm sorry to hear about all the problems your having getting your little one off to school. I'm not expect, although I do have 2 children myself, one that just started pre-school and was doing the exact same thing.
I’m just going to throw in my 2-cents here, so bare with me.
First off I wouldn’t punish him for it, I doubt it’s for show. He is having anxiety about it himself and in a panic. I doubt disciplining him for it would help how he feels. So the problem is still going to keep happening.
I know he is only in first grade, but what are his reasons for not wanting to go? My 4 year old will tell me at least why she is scared of things. Although his answer may not be anything you can help. You could at least comfort him on the subject and just give him some reassurance.
Secondly I can promise you this will eventually ease up and pass all together. Now if he was very young, say 2 years old he might continue to scream and cry forever. But he is at an old enough age to figure things out on his own, and relies school isn’t so bad.
My youngest did eventually stop being so upset in the mornings; it just took about 2 months. My wife gets way more upset on drop-offs then me because I just always keep in my mind that it’s for her best interest. And in your Childs ages’ case, it’s the law. So there isn’t too much you can do but comfort her and give it time.
Good Luck with it, and no worries it will improve