Generally private schools have the ability to expel students for many various reasons.  Because they are a private school, they have much greater ability to do this than a public school.  A lot depends upon the school guidelines and code of conduct and any written agreement you have with the school with respect to your son's enrollment.  Without seeing those documents, it is difficult to advise you as to what, if anything, you can do.  It is possible that the school does not have to re-admit your son if they do not wish to.