Nowadays, humanity has to face the problem of constantly increasing amounts of waste, which cause not only environmental pollution but also poses a critical danger to human health. Moreover, the growth of landfill sites involves high costs of establishment, development, and maintenance. Glass is one of the materials whose recycling ratio is still insufficient. Therefore, in the presented work, the influence of the particle size and share of waste glass on the consistency, morphology, specific surface area, water absorption, setting time, and mechanical properties of geopolymers was determined. Furthermore, for the first time, the fire resistance and final setting time of such geopolymer composites were presented in a wide range. Based on the obtained results, it was found that the geopolymer containing 20% unsorted waste glass obtained a final setting time that was 44% less than the sample not containing waste glass, 51.5 MPa of compressive strength (135.2% higher than the reference sample), and 13.5 MPa of residual compressive strength after the fire resistance test (164.7% more than the reference sample). Furthermore, it was found that the final setting time and the total pore volume closely depended on the additive’s share and particle size. In addition, the use of waste glass characterized by larger particle sizes led to higher strength and lower mass loss after exposure to high temperatures compared to the composite containing smaller ones. The results presented in this work allow not only for reducing the costs and negative impact on the environment associated with landfilling but also for developing a simple, low-cost method of producing a modern geopolymer composite with beneficial properties for the construction industry.