Nanocomposites based on attapulgite clay and shape-memory polyurethane were fabricated by mechanical mixing. The mechanical properties of samples were evaluated using a micro-indentation tester. The untreated commercial attapulgite clay resulted in a significant decrease in glass transition temperature and hardness of the nanocomposite due to the presence of moisture as well as the clay’s amorphous structure and surface hydroxyl groups. The attapulgite nanoparticles were heat-treated at 850 °C, which resulted in crystallization of the particles and formation of layered attapulgite structure. The hardness of the nanocomposites composed of the heat treated clay powder dramatically increased as a function of clay content, which is attributed to the homogeneous dispersion of the nanofillers in the polymer matrix and strong filler–polymer interactions. Shape recovery of indentations has been demonstrated upon heating.