Laser welding and nanocomposites are finding increasing applications in industries. The polypropylene/ethylene-propylene-diene-monomer/clay nanocomposite has wide application in many industries. In this study, the effect of laser power, standoff distance, scan velocity, and clay content as input parameters on tensile and impact strengths of laser welds and welding operation cost as output parameters has been investigated using response surface methodology. The Box–Behnken design was employed to establish proper mathematical models relating input to output parameters. Morphology and dispersion of clay in the above nanocomposite have also been evaluated by X-ray diffraction and transmission electron microscopy. The results have been presented numerically and graphically. The results show that with laser power of 108.84–110.90 W, scan velocity of 566.18–597.19 mm/min, standoff distance of 8 mm, and clay content of 0.35–0.83 wt%, optimum values for tensile strength of 9.3 MPa, impact strength of 67.2 J/m, and welding cost of 30 cents/m are obtained. A minimum cost weld (18.5 cents/m) can be achieved when a proper combination of laser power of 108.53–109.80 W, scan velocity of 874.27–893.09 mm/min, standoff distance of 8 mm, and clay content of 0.75–0.94 wt% is selected.