Poly(ethylene-vinyl acetate) (PEVA) nanocomposite incorporating dual clay nanofiller (DCN) of surface modified montmorillonite (S-MMT) and bentonite (Bent) was studied for biomedical applications. In order to overcome agglomeration of the DCN, the S-MMT and Bent were subjected to a physical treatment prior to being mixed with the copolymer to form nanocomposite material. The S-MMT and Bent were physically treated to become S-MMT(P) and Bent(pH-s), respectively, that could be more readily dispersed in the copolymer matrix due to increments in their basal spacing and loosening of their tactoid structure. The biocompatibility of both nanofillers was assessed through a fibroblast cell cytotoxicity assay. The mechanical properties of the neat PEVA, PEVA nanocomposites, and PEVA-DCN nanocomposites were evaluated using a tensile test for determining the best S-MMT(P):Bent(pH-s) ratio. The results were supported by morphological studies by transmission electron microscopy (TEM) and scanning electron microscopy (SEM). Biostability evaluation of the samples was conducted by comparing the ambient tensile test data with the in vitro tensile test data (after being immersed in simulated body fluid at 37 °C for 3 months). The results were supported by surface degradation analysis. Our results indicate that the cytotoxicity level of both nanofillers reduced upon the physical treatment process, making them safe to be used in low concentration as dual nanofillers in the PEVA-DCN nanocomposite. The results of tensile testing, SEM, and TEM proved that the ratio of 4:1 (S-MMT(P):Bent(pH-s)) provides a greater enhancement in the mechanical properties of the PEVA matrix. The biostability assessment indicated that the PEVA-DCN nanocomposite can achieve much better retention in tensile strength after being subjected to the simulated physiological fluid for 3 months with less surface degradation effect. These findings signify the potential of the S-MMT(P)/Bent(pH-s) as a reinforcing DCN, with simultaneous function as biostabilizing agent to the PEVA copolymer for implant application.