At elevated temperatures, glasses crystallize via thermally activated diffusion. However, metallic glasses can also undergo deformation-induced crystallization at very low temperatures. Here we demonstrate the crystallization of Al50Fe50 metallic glasses under cyclic deformation at 50 K using molecular dynamics simulations and reveal the underlying atomic-scale processes. We demonstrate that stress-driven nonaffine atomic rearrangements, or shear diffusion transformation (SDT) events, lead to successive metabasin-to-metabasin transitions and long-range ordering. We also illustrate that the nucleation and growth of the crystal proceed via collective attachment of ordered clusters, advancing the amorphous/crystal interface in an intermittent manner. The cooperative nature of the steplike crystallization is attributed to the large activation volume of Eshelby transformations which generate as a by-product nonaffine diffusive atomic displacements that accumulate over loading cycles. The dual nature of shear (affine) and diffusion (nonaffine) in low-temperature stress-driven SDT events thus unifies inelasticity with crystallization.