Engineered geopolymer composite (EGC) is a high-performance material with enhanced mechanical and durability capabilities. Ground granulated blast furnace slag (GGBFS) and silica fume (SF) are common binder materials in producing EGC. However, due to the scarcity and high cost of these materials in some countries, sustainable alternatives are needed. This research focused on producing eco-friendly EGC made of cheaper and more common pozzolanic waste materials that are rich in aluminum and silicon. Rice husk ash (RHA), granite waste powder (GWP), and volcanic pumice powder (VPP) were used as partial substitutions (10–50%) of GGBFS in EGC. The effects of these wastes on workability, unit weight, compressive strength, tensile strength, flexural strength, water absorption, and porosity of EGC were examined. The residual compressive strength of the proposed EGC mixtures at high elevated temperatures (200, 400, and 600 °C) was also evaluated. Additionally, scanning electron microscope (SEM) was employed to analyze the EGC microstructure characteristics. The experimental results demonstrated that replacing GGBFS with RHA and GWP at high replacement ratios decreased EGC workability by up to 23.1% and 30.8%, respectively, while 50% VPP improved EGC workability by up to 38.5%. EGC mixtures made with 30% RHA, 20% GWP, or 10% VPP showed the optimal results in which they exhibited the highest compressive, tensile, and flexural strengths, as well as the highest residual compressive strength when exposed to high elevated temperatures. The water absorption and porosity increased by up to 106.1% and 75.1%, respectively, when using RHA; increased by up to 23.2% and 18.6%, respectively, when using GWP; and decreased by up to 24.7% and 22.6%, respectively, when using VPP in EGC.