This study developed a biodegradable composite porous polyurethane scaffold based on polycaprolactone and polyethylene glycol by sequential in-situ foaming salt leaching and freeze-drying process with responsive shape changing performance. Biomineral hydroxyapatite (HA) was introduced into the polyurethane matrix as inorganic fillers. Infrared spectroscopy results proved a successful synthesis, scanning electron microscopy showed that the scaffold’s porosity decreased with the addition of HA while the average pore size increased. X-ray diffraction and differential scanning calorimetry showed that the addition of HA lowered the melting point of the scaffold, resulting in a transition temperature close to the human body temperature. From the bending experiments, it could be demonstrated that PUHA20 has excellent shape memory performance with shape fixity ratio >98.9% and shape recovery ratio >96.2%. Interestingly, the shape-changing capacity could be influenced by the porous structures with variation of HA content. The shape recovery speed was further accelerated when the material was immersed in phosphate buffered saline at 37 °C. Additionally, in vitro mineralization experiments showed that the scaffold incorporating HA had good osteoconductivity, and implantation assessment proved that scaffolds had good in vivo biocompatibility. This scaffold is a promising candidate for implantation of bone defects.