In recent decades, turning solid wastes/by-products from agricultural and industrial activities into useful construction materials has been received much attention from many researchers in the world. Following this trend, this study reused copper mine tailings (CMT) as a fine aggregate in combination with fly ash and ground granulated blast-furnace slag (GGBFS) as binder materials to produce fine-grained concrete (FGC). Before being used, the CMT was checked for heavy metal concentration and the result confirm that CMT is a non-toxic material. Then, the FGC samples were prepared with a fixed water-to-binder ratio of 0.23 and the effects of various contents of CMT (55, 65, and 75% by weight) and GGBFS (4, 8, and 12% by weight) on the workability, compressive strength, and cost-effectiveness of the FGC were evaluated in this study. The experimental results showed that both CMT and GGBFS had a large influence on the engineering performance of FGC. Indeed, although increasing CMT content up to 65% in the FGC mixture caused a slight reduction in workability, the compressive strength of the 28-day FGC samples was slightly increased. However, the FGC samples containing 75% CMT exhibited lower compressive strength than that of others. On the other hand, the incorporation of more GGBFS enhanced both the workability of the fresh FGC mixtures and the 28-day compressive strength of the hardened FGC samples. It is found that a maximum compressive strength value of 37.5 MPa was obtained at the FGC sample containing 12% GGBFS and 65% CMT. Moreover, the cost analysis result also pointed out that using CMT and GGBFS in the FGC production was cost-effective. As a result, this study further demonstrated the high feasibility of the re-utilization of both CMT and GGBFS in the production of FGC toward sustainable development.