In the present study, the effectiveness of four polymers grafted with maleic anhydride used as compatibilizers in blends with poly(lactic acid) and its composites with sepiolite as matrices was evaluated in terms of transmission and scanning electron microscopy, oscillatory shear flow and tensile properties. Two polypropylenes were used as dispersed phases in the blends prepared in a corotating twin-screw extruder. Results showed that the compatibilized blends prepared without clay have higher susceptibility to isothermal degradation and higher tensile toughness than those prepared with sepiolite. The blend with the grafted metallocene polyethylene as compatibilizer exhibited the highest tensile toughness. The composites based on polyblends with polypropylene displayed lower tensile strength and Young's modulus values, increased values of elongation at break, tensile toughness, complex viscosity, and storage modulus compared to those of the nanocomposite of PLA. These results are related to the clay dispersion, to the type of morphology of the different blends, to the grafting degree of the compatibilizers, and to the migration of the sepiolite toward the PP interface.