To address the challenge of mitigating heavy metal pollution stemming from the utilization of industrial solid wastes like copper tailings, this study focused on the development of copper tailings-granulated blast furnace slag (CT-GBFS) geopolymer through alkali activation. The primary objective was to effectively immobilize heavy metals, specifically copper (Cu) and zinc (Zn), within the geopolymer. This investigation encompassed an exploration of how Cu and Zn impacted the mechanical properties of CT-GBFS geopolymer, along with an analysis of the leaching behavior of these heavy metals in various environmental conditions. The study also delved into the underlying mechanisms responsible for immobilizing these heavy metals. The experimental findings revealed that the inclusion of up to 2% heavy metals could enhance the mechanical properties of geopolymer. However, as the heavy metal content increased, a detrimental effect on the mechanical properties became evident. Furthermore, CT-GBFS geopolymer exhibited excellent heavy metal immobilization capabilities across different environmental conditions. Specifically, the immobilization rate for copper exceeded 98%, while zinc exhibited an immobilization rate exceeding 93%. The geopolymer has a physical encapsulation fixation mechanism for both Cu and Zn. Additionally, copper was observed to form a covalent bond with non-bridging oxygen in the geopolymer, manifesting as a Si–O–Cu structure, thereby effectively immobilizing the metal. Conversely, zinc was immobilized within the geopolymer through ionic bonding. In conclusion, the technology proposed in this study represents a significant step toward achieving the safe and resourceful utilization of copper tailings by effectively immobilizing heavy metals, thus mitigating their environmental impact.