Final answer:
According to Mintzberg's typology, the CEO is performing the role of a disturbance handler by taking responsibility for the environmental damage caused by the oil spill.
Step-by-step explanation:
When the CEO of an American petroleum company took responsibility for correcting the environmental damages caused by his company following an oil spill in the Gulf of Mexico, according to Mintzberg's typology, he is performing the role of a disturbance handler. This role involves dealing with unforeseen problems and crises that an organization faces, including handling major disturbances like an oil spill. As a disturbance handler, the CEO is required to take corrective action and to manage the resolution of the crisis, a task that lies at the heart of this managerial role.