In the People and Employees section of the company's Admin tab, select the director whose relationship you wish to edit, click on the cogs, and click edit:
In the form that opens, scroll down to the Roles and Responsibilities section, and next to 'Directorship', select Remove as director. Put in the last date at which the person is to be recorded as a director (i.e. the day before which the removal becomes effective), and click Save.
From the date the removal becomes effective, the person will no longer be recorded as a director:
After removing them, the dates at which the person held the directorship will be recorded in their profile: