The present disclosure relates to a process by which an optical fiber array is cleaved with a laser-cleaving apparatus. The coating material is stripped or removed from a section of an optical fiber array; a coated or ribbonized section of the optical fiber array is secured in a holder; the holder is aligned inside the laser-cleaving apparatus; the laser cleaves the stripped ends of the fibers in the optical fiber array; the laser-cleaved ends of the optical fibers are then mechanically separated to remove the free ends from the optical fibers in the optical fiber array, leaving a cleaved array of optical fibers. The cleaving process enables the optical fiber array to be cleaved at flexible locations along an optical fiber ribbon or optical fiber cable with no swelling, minimal cleave angle variation across the cores of the optical fibers, a controlled surface roughness of the optical fiber end-faces, and high process yield.