In 1767 he went to the Baja California Peninsula and was placed in charge of the Misión La Purísima Concepción de Cadegomó.

He traveled in the vanguard of the land expedition to San Diego, led by Captain Fernando Rivera y Moncada, where a presidio and mission were established.

In 1772, Crespí accompanied Captain Pedro Fages on an exploration of areas to the east of San Francisco Bay.

In 1774, Crespí was chaplain of the expedition to the North Pacific conducted by Juan José Pérez Hernández.

One chapel he built, at the Misión San Francisco del Valle de Tilaco in Landa, is reported as still standing.