I am a teacher, albeit secondary.
It is incredibly annoying when pupils get involved when I'm disciplining pupils. It just adds to the disruption, because then I need to deal with the pupil who's decided to get involved as well. You can see how this can escalate rapidly.
The teacher needed him out of the classroom so she could deal with the existing dispute, before talking to your son. There is no reason to think she wouldn't have let him explain what happened when she got round to talking to him. However, it sounds like your son wanted to explain why he had laughed right that very second, instead of following the teacher's instructions and leaving the classroom quietly. So now not only has he got involved in other people's business, but when he is pulled up on this, he starts arguing and doesn't follow instructions, and the situation has escalated rapidly. Extremely disruptive. Do not minimise defiant behaviour, it's really problematic!
It's not clear from your post that it was anxiety causing his reaction. If it was, you need to make sure that he understands why he is being asked to stand outside. If he can't, you need to come up with alternatives together with the teacher. Maybe he could be asked to move to a different desk instead, until the teacher has spoken to him? Asking the teacher not to discipline him and saying you'll do it instead is, quite frankly, bonkers, sorry.
I am not an SEND specialist, but I have taught pupils who behaved similarly. Sometimes it's "just" rudeness/ bad behaviour (not knowing when to be quiet and follow instructions, rather than arguing). Other times it's ADHD. In fact, it really reminds me of a pupil I teach with ADHD. It's not just being hyper, there's much more to it. It might be worth exploring.
Good luck!