Multiblock copolymers consisting of crystalline poly(butylene succinate) and amorphous poly(1,2-propylene succinate) (PBS-co-PPS) are synthesized. The microstructure of the materials is investigated by the combination of thermal analysis and wide-angle/small-angle X-ray scattering (WAXS/SAXS). The noncrystalline PPS blocks are found to locate predominately in the amorphous phase between crystalline lamellae of PBS. By means of in situ WAXS coupled with optical-assisted strain measurement, the deformation process of PBS-co-PPS is studied. The stiffness and strength of PBS-co-PPS decrease with increasing PPS fraction, while the strain recovery behavior of PBS-co-PPS is similar to PBS homopolymer. Transition from alpha crystal to beta crystal is observed for all the PBS-co-PPS samples. The critical stress for alpha-beta transition of PBS-co-PPS is determined, which is found to be independent of PPS blocks. The universal critical stress for crystal transition is interpreted through a single-microfibril-stretching mechanism.