Can 2 of three officers remove the CEO who is also executive director of a mutual benefit nonprofit Corp.?

Officers do not remove officers; directors remove officers. You may have many legal issues regarding breach of fiduciary duty. You should consult a local attorney since such analysis would be beyone the scope of a site like this. 

The owners elect the members of the Board of Directors, and the Board of Directors hires or appoints the officers, including CEO, CFO, Secretary and any Vice Presidents and any Executive Director. Only the Board of Directors, acting as the Board of Directors, can fire any officer. That means there must either be notice of a meeting and a vote at the meeting, or a unanimous written consent. Only the owners, voting pursuant to a written ballot sent in advance of the meeting, can remove any member of the Board of Directors. However, you mention an agreement among 4 owners. Owners can enter into agreements to vote their ownership shares as provided in the agreement. For example, I represented a company owned by three families in different shares, and they agreed in writing that each family would choose a family member to belong to the Board of Directors, and all of the owners would vote their shares telect the three driectors designated by the families. Your post could be interpreted to mean that there are other owners, in addition to the four prinicpal owners who agreed. Removing directors requires special percentages of voting. If there are other owners, then the four principal owners might or might not have enough votes to remove director without the votes of the other owners. You need to hire an attorney to go over the company's governing documents, ownership interests, and minutes, to advixe you on everyone's rights and how to exercise those rights properly. For example, voting by owners is done by secret ballots sealed in two envolopes and counted at a meeting of the owners. It is not done by a show of hands. Dana Sack