Section 63.43 shall not apply to removals of persons in any department of the city where the department is under the supervision and control of a board or commission of 3 or more members, but every such board or commission shall establish rules relating to the removal, discharge or reduction of employees in its department. No such employee shall be removed, discharged or reduced for religious or political reasons and any removed, discharged or reduced employee shall have the right to a trial and determination by the board or commission, or by a committee duly appointed by the board or commission as to whether there existed sufficient grounds for removal, discharge or reduction and the determination of the board or commission, or of the committee when approved by the board or commission, shall be final in the matter. The right of suspension is granted boards and commissions included under this section the same as is elsewhere provided for in ss. 63.18 to 63.53.