Polylactic acid has stood out among bio-based polymers for its usage in the food packaging industry and biomedical fields. Through the melt mixing process, the toughened poly(lactic) acid (PLA) was prepared with polyolefin elastomer (POE), incorporated via various ratios of nanoclay and a fixed amount of nanosilver particles (AgNPs). The correlation between the compatibility and morphology, mechanical properties, and surface roughness of samples with nanoclay was studied. The calculated surface tension and melt rheology confirmed the interfacial interaction demonstrated by droplet size, impact strength, and elongation at break. Each blend sample exhibited matrix-dispersed droplets, and the size of POE droplets steadily dropped with increasing nanoclay content, corresponding to the enhanced thermodynamic affinity between PLA and POE. Scanning electron microscopy (SEM) acknowledged that the inclusion of nanoclay in the PLA/POE blend ameliorated the mechanical performance by preferable localization in the interface of used components. The optimum value of elongation at break was acquired at about 32.44%, where the incorporation of 1 wt.% nanoclay led, respectively, to 171.4% and 24% enhancement rather than the PLA/POE blend with the composition of 80/20 and the virgin PLA. Similarly, the impact strength reached 3.46 ± 0.18 kJ m−1as the highest obtained amount, showing the proximity of 23% progress to the unfilled PLA/POE blend. Surface analysis indicated that adding nanoclay caused the augment of surface roughness from 23.78 ± 5.80 µm in the unfilled PLA/POE blend to 57.65 ± 18.2 µm in PLA/POE contained 3 wt.% nanoclay. Rheological measurements implied that organoclay resulted in the strengthening of melt viscosity as well as the rheological parameters such as storage modulus and loss modulus. Han plot further showed that the storage modulus is always higher than the loss modulus in all prepared PLA/POE nanocomposite samples, corresponding to the restriction of polymer chains mobility induced by the formation of strong molecular interaction between nanofillers and polymer chains.