In the first instance, the chair has the power to order a disruptive non-member to leave the room on his own initiative. (RONR 11th ed., p. 648, ll. 14-21.) ("Non-member", here, refers to someone who is not a member of the body that is meeting at that moment, so at a board meeting, it means anyone who is not a member of the board.) A motion to exclude all non-members (except absolutely necessary staff, if necessary) is often referred to as a motion to "go into executive session" (RONR 11th ed., p. 645, ll. 1-3). But I don't see a reason why the board cannot just exclude non-members by motion without adopting the secrecy of the executive session, given that the same result can be achieved by going into executive session and then immediately resolving to lift the secrecy attached.