If a student is either so disruptive that he/she is preventing others from learning or their personal attributes (vaccination, carrying a communicable disase etc) put others at risk, than not only is it “allowed” to suspend them from school but the school administrators are obligated to do so. It is mamash gazalah from the other parents who are being mesiras nefesh to pay the tuition to educate their kids to allow a chronically disruptive student to remain in school and deny chinuch to others. Likewise it is pikuach nefesh to protect the other kids from one who poses a known medical risk.
The real question is what responsibility does the tizbur in general have to provide the financial support for special education in terms of either home schooling etc. for those who cannot be allowed to attend regular yeshivos/beis yaakovs.