X-ray diffraction (XRD) and transmission electron microscope (TEM) investigations have been carried out to decode the influence of stacking-fault energy (SFE) on the accommodation of large shear deformation in Cu-Al alloys subjected to one-pass equal-channel angular pressing. XRD results exhibit that the microstrain and density of dislocations initially increased with the reduction in the SFE, whereas they sharply decreased with a further decrease in SFE. By systematic TEM observations, we noticed that the accommodation mechanism of intense shear strain was gradually transformed from dislocation slip to deformation twin when SFE was lowered. Meanwhile, twin intersections and internal twins were also observed in the Cu-Al alloy with extremely low SFE. Due to the large external plastic deformation, microscale shear bands, as an inherent deformation mechanism, are increasingly significant to help carry the high local plasticity because low SFE facilitates the formation of shear bands.