Thermoplastic polypropylene (PP) has garnered a significant attention in power cable insulation research because of its exceptional thermal tolerance and dielectric properties. Due to its poor impact strength at room temperature, PP has been blended with various elastomers, including ethylene-propylene-diene monomer (EPDM), to improve the mechanical stiffness of the final material. This, however, comes with compromised dielectric properties of the material. Recently, the addition of nanofillers to polymers has demonstrated promising properties that can be tailored for various dielectric applications, provided that nanofiller and polymer interactions are appropriately formulated. Nevertheless, the effect of nanostructuration in PP/elastomer blends, especially from the perspective of dielectrics, have yet to be systematically explored. In the current work, magnesia (MgO) nanofiller is added to a model PP/EPDM blend system to determine the effect of MgO on the breakdown properties of PP/EPDM. The results show that adding 0.5 wt% of MgO to PP/EPDM reduces the AC and DC breakdown strengths by 7% and 16%, respectively. As the amount of MgO increases to 3 wt%, the AC and DC breakdown strength reduces further by 25% and 29%, respectively. Significantly, appropriate modification of the nanocomposites with polypropylene-graft-maleic anhydride (PP-g-MAH) can result in 5% higher breakdown strength of the nanocomposites with respect to comparable nanocomposites without modification. The mechanisms surrounding these breakdown effects are discussed with the aid of materials structure interpretations. Overall, the results demonstrate that appropriate modification of nanocomposites with PP-g-MAH is crucial in tailoring breakdown properties of PP blend nanocomposites.