Can a school board not allow you to participate in a Graduation Exercise due to a outside arrest for drug dealing when I was a juvenile.
Simple answer... yes. 'Walking' is a privilege not a right. The school board cannot prevent him from receiving a diploma if he has completed the requirements but is not prohibited from restricting his extra activities.
And can they stop you from attending classes after suspension for this
If he meets the requirements to graduate, why is he 'attending classes'?? The school year is virtually over.
However, to answer your question, they can certainly suspend or expel a student for conduct. As for 'stopping him', no. They will provide alternate education 'services'.