When a corporation goes into business, they must file an Articles of Incorporation. According to the US Legal website, the Articles of Incorporation is a document that must be filed with the state in order to incorporate. Information included in the document includes the company name, location and names of the officers of the company.
If the officers change for any reason, then a new incorporation document, referred to as a Restated Articles of Incorporation, must be filed.
Take a vote. If the officer is asking to be removed from the Articles of Incorporation, then the vote would be for informational purposes for the minutes of the meeting. However, if other officers are calling for this individual's removal, then the officers who want him removed state their case, the officer being removed defends his position, and then the board votes on the removal. A majority vote determines whether the officer is removed or not.
Have the officer sign a letter of resignation. If the officer resigned voluntarily, he should create the resignation citing his reasons for resigning. If he was voted out, the remaining officers should draft the resignation stating why the officer was removed.
Take another vote. If the officer is to be replaced, a new officer will need to be nominated and voted in. This is optional unless the business charter requires a set number of members.
File a restated Articles of Incorporation including the new officer. A new Articles of Incorporation needs to be filed with the state's secretary of state office, removing the old officer and adding a new one if a new one was added.