The micromechanical deformation mechanisms of a polylactic acid (PLA)/natural rubber (NR) blend (PLA/NR 90/10 wt%) and its organoclay filled bionanocomposites have been investigated by small and wide angle X-ray scattering (SAXS–WAXS) under tensile conditions. The addition of NR to a PLA matrix changed the brittle fracture of PLA to a ductile deformation through the debonding of the rubber droplets. Otherwise, the formation of cavities between PLA and NR was hampered by the nanoclays since they were mainly located at the polymer blend interface. In this case, the nanoclays acted as craze nucleation sites. At 1 wt% of filler concentration, the crazes were able to fully develop in the blend and to evolve into stable microvoids, which kept growing and orienting in the tensile direction. These mechanisms also explained the progressive plastic deformation of the polymer chains and the preferential orientation of the nanoclay platelets.