The unique control mechanisms of the plastic deformation of two-phase extruded alloy composed of Mg and long-period stacking ordered (LPSO) phase were clarified by comparison with those of other Mg solid-solution alloys, focusing on the question “why do the Mg/LPSO two-phase alloys exhibit both large elongation and high strength?”. The stress-strain curves for each grain in the alloys could be imaginary estimated using neutron diffraction analysis during the tensile test. The results demonstrate that the deformation behaviors of the worked and recrystallized grains are significantly different in all the Mg-extruded alloys owing to the strong plastic anisotropy in Mg with hexagonal close-packed (hcp) structure. Therefore, the deformation behavior is controlled by a composite-like deformation mechanism, even in single-phase Mg solid-solution alloys. In Mg-Y-Zn ternary alloys, the recrystallized Mg grains exhibited significant lattice softening at the initial stage of yielding owing to the escape of basal dislocations from the Y/Zn dragging atmosphere. However, the worked grains acted as strengthening components. In the Mg/LPSO two-phase alloy, the composite-like deformation behavior was enhanced, and the LPSO phase significantly contributed to the strengthening of the alloy. Moreover, it was hypothesized that the LPSO phase contributes not only to the alloy's strength but also to its elongation by increasing the work-hardening rate. We proposed the new concept “Anisotropic Mechanical property-Induced Ductilization (AMID)” by multimodal microstructure, to explain this phenomenon. As the physical origin for inducing AMID, kink-band strengthening in the LPSO phase is believed to be one of the reasons for the increase in the work-hardening rate of the extruded LPSO-phase grains in the Mg/LPSO two-phase alloy, resulting in an improved ductility.