Three types of composites, namely, polylactide (PLA)/nanoclay, PLA/core-shell rubber, and PLA/nanoclay/core-shell rubber, were melt compounded via a corotating twin-screw extruder. The effects of two types of organically modified montmorillonite nanoclays (i.e., Cloisite(R)30B and 20A), two types of core (polybutylacrylate)-shell (polymethylmethacrylate) rubbers (i.e., Paraloid EXL2330 and EXI-2314), and the combination of nanoclay and rubber on the mechanical and thermal properties of the composites were investigated. According to X-ray diffraction and transmission electron microscopy analyses, both types of PLA/5 wt% nanoclay composites had an intercalated morphology. In comparison with pure PLA, both types of PLA/5 wt% nanoclay composites had an increased modulus, similar impact strength, slightly reduced tensile strength, and significantly reduced strain at break. On the other hand, PLA/EXL2330 composites with a rubber loading level of 10 wt% or higher had a much higher impact strength and strain at break, but a lower modulus and strength when compared with pure PLA. The simultaneous addition of 5 wt% nanoclay (Cloisite(R)30B) and 20 wt% EXL2330 resulted in a PLA composite with a 134% increase in impact strength, a 6% increase in strain at break, a similar modulus, and a 28% reduction in tensile strength in comparison with pure PLA.