I think you really need to try to be more supportive of the school. Your ds will clearly pick up that you do not back-up the school and this undermines all their behavioural policies.
Many/most students will come with all sorts of stories, exaggerations, fabrications when confronted by their parents about incidents/punishments at school. Do you really think teachers make this stuff up?
Exclusions are serious matters, and are all counted (negatively) in statistics for Ofsted and so on. Schools do not exclude lightly.
In this case (from your son's report) you say the students were told to be quiet and move along, but they continued to shout and your son laughed. Whatever your son actually did, a member of staff was present and witnessed it, and it was viewed to be serious enough to merit an exclusion. In these circumstances I would believe a member of staff over a teenager any day, even an outraged, indignant "I didn't do it" teenager. Because I've seen teenagers argue till their blue in the face about something I have just witnessed them do!
At my school the most unpleasant students we have to deal with are the ones who have learned that whatever happens their parents will believe their stories, and will not believe the school or back up the school in any way. They have no respect for school staff, and can behave appallingly at times.
I have said to my boys that if they are in trouble at school for something or have a detention or whatever, they needn't even think about coming home and saying "I didn't do it. It wasn't me!" And that even if occasionally they receive an unjust punishment they will have to take it on the head.
How old is he btw?
Why not just give my approach a try? Just suspend your belief, imagine the school is correct and your son is spinning you a line. Go into school and listen to their version. Tell your son you are appalled and shocked at his behaviour. Explain to him that you do not believe that the member of staff would make up such a story. Just give the school your support, and see what impact it has on your son's future behaviour.