In this study, to reduce the amount of cement consumed in the production of cementitious composites, the effects of partial replacement of cement weight with nano-silica, silica fume, and copper slag on the mechanical properties of polypropylene fiber-reinforced cementitious composites are investigated. For this purpose, the effect of replacing cement weight by each of the aforementioned materials individually and in combination is studied. A total of 34 mix designs were prepared, and their compressive, tensile, and flexural strengths were obtained for each mix. Among the mix designs with one cement replacement material, the highest strength is related to the sample containing 2.5% nano-silica. In this mix design, the compressive, tensile, and flexural strengths improve by about 33%, 13%, and 15%, respectively, compared to the control sample. In the ones with two cement replacement materials, the highest strengths are related to the mix made with 10% silica fume along with 2% nano-silica. In this mix design, compressive, tensile, and flexural strengths increase by about 42%, 18%, and 20% compared to the control sample, respectively. Furthermore, in the mixtures containing three cement substitutes, the final optimal mix design for all three strengths has 15% silica fume, 10% copper slag, and 2% nano-silica. This mix design improves the compressive, tensile, and flexural strengths by about 57%, 23%, and 26%, respectively, compared to the control sample. Finally, two relationships have been presented that can be used to predict the values of tensile and flexural strengths of cementitious composites with very good accuracy only by determining the compressive strength of the composites.