Globally, there is an increasing attention drawn by copper tailings (CT) due to the environmental problems caused by its tremendous storage volume and low recycling rate. With the purpose of promoting the sustainability and value-added utilization of CT, this study used CT powder with particle size ≤ 0.075 mm, granulated blast furnace slag (GBFS), and fly ash (FA) to prepare CT/FA-GBFS geopolymer paste composites. Also, 0.075–0.6 mm CT sand was also used as a replacement of natural fine aggregates. The effect of CT powders on the mechanical strength of the geopolymer paste was assessed, as well as the influence of CT sand on the mechanical strength and the heavy metal leaching behavior of CT-GBFS geopolymer mortar. The obtained results from the study demonstrate that CT powder exhibits partial participation in the geopolymerization reaction within an alkaline environment. Additionally, it manifests a filling effect when incorporated as micro powders. It is noteworthy that the compressive strength of the geopolymer paste improved by 18% and the flexural strength by 74% when the CT content reached 45%. Furthermore, in the context of CT-GBFS geopolymer mortar, the 20% replacement ratio of CT sand yields a more favorable interfacial transition zone (ITZ) between the geopolymer paste and the mixed sand. This improved ITZ improves the mechanical properties of the mortar by about 10% compared to other experimental groups. Finally, when CT were immobilized in the CT-GBFS geopolymer mortar, the leaching of heavy metals from copper tailings was significantly reduced, eliminating the impact of CT utilization on the environment.