Managing basalt rock cutting waste in an environmentally responsible manner is crucial to mitigate its negative impacts and protect both the environment and human health. Recycling basalt rock cutting waste in geopolymer applications offers multiple environmental, economic, and performance benefits, making it a promising approach for sustainable construction practices. For this purpose, this study concerns about the performance of fiber-reinforced basalt rock-cutting waste-based geopolymer composites at high temperatures up to 1000 °C. Geopolymer composites were manufactured by activating basalt rock cutting waste with sodium silicate. Alongside the fiber-free mixtures, fiber-reinforced geopolymer composites incorporating 0.5% and 1.0% basalt or polypropylene fibers by volume were synthesized. These composites underwent thermal curing at 100 °C for two distinct durations: 8 h and 24 h. In addition, the geopolymer composites were subjected to thermal exposure at three different temperatures: 600 °C, 800 °C, and 1000 °C. Changes in the strength and weights of the composites were determined after high-temperature exposure. In addition, XRD and SEM/EDX analyses were performed on the selected composites to investigate the changes in the microstructure of the composites. Thermal curing time and fiber content had significant influence on the high-temperature performance of the geopolymer composites. In this study, geopolymer mortars based on basalt rock cutting waste were successfully developed, demonstrating resistance to elevated temperatures up to 1000 °C. No reduction in compressive strength was observed in any of the composites when exposed to 600 °C, 800 °C, and 1000 °C. In fact, an increase in strength was recorded at varying rates, compared to the pre-exposure values.