He was military commander of the kingdoms of Aragon and Mallorca when he was named viceroy, captain general and president of the Audiencia of New Spain.

Acuña found a nearly empty treasury and a great public debt, and it was necessary that he pay special attention to the finances of the colony.

Acuña also pacified completely the region of Nayar, sending an armed expedition there under Juan Flores de San Pedro and establishing colonies.

During his tenure as viceroy, British colonists began establishing settlements in Spanish-controlled Yucatan and Central America to harvest tropical timber.

However, after they arrived at the settlements, the Spanish realised the British could muster 800 men and several large ships to oppose them, and ultimately retreated.

Spanish diplomatic efforts to terminate the British presence in the region were also unsuccessful, and Acuña decided to let the matter drop.

Instead, he focused on strengthening the military of New Spain, including the garrisons at San Juan de Ulúa, Isla del Carmen, Veracruz, and the bays of Espíritu Santo and Pensacola.