Steel slag (SS), an industrial by-product of the steel industry, has the potential to serve as a natural aggregate alternative in concrete production to not only mitigate the exploitation of natural resources but also minimize the environmental impact of its treatment and disposal. This study was designed to investigate comprehensively the impacts of using SS as a full replacement for coarse aggregate and of using fly ash (FA) and ground granulated blast-furnace slag (GGBFS) as partial replacements for Portland cement on the engineering properties (i.e., workability, fresh unit weight, porosity, compressive and flexural strengths, ultrasonic pulse velocity, and drying shrinkage), durability (i.e., water absorption, surface electrical resistivity, and rapid chloride ion penetration), and microstructure (i.e., scanning electron microscopy observation) of high-performance concrete (HPC). A comparative analysis of the economic and environmental benefits of SS concrete versus natural aggregate concrete was also performed. The test results revealed that SS, FA, and GGBFS all impacted the properties of HPC significantly. The HPC mixtures in which natural aggregate had been completely replaced with SS exhibited about 20.4–21.3% higher unit weight than the natural aggregate concrete. The HPC samples with added FA and GGBFS exhibited enhanced performance in terms of mechanical strength, durability, and microstructure. Moreover, total material cost, global warming potential (GWP), and ozone depletion potential (ODP) were all found to be significantly lower in the HPC samples produced using SS and either GGBFS or a combination of FA and GGBFS. As a result, after 210 days of normal curing, the 100% SS concrete containing 15% FA and 35% GGBFS as a Portland cement substitution (S100F15G35 specimen) exhibited compressive and flexural strength values of 110.3 and 11.1 MPa, which were approximately 9.0% higher than the corresponding values of the reference concrete. Also, the S100F15G35 specimen registered the respective ultrasonic pulse velocity, surface electrical resistivity, and rapid chloride ion penetration values of 5328 m/s, 113.3 kΩ.cm, and 203 Coulombs, indicating high-quality and durable concrete. Moreover, incorporating 15% FA and 35% GGBFS in SS concrete resulted in a reduction of 15.7% drying shrinkage and 24.4% total material cost, especially reduced environmental impacts with a significant reduction in GWP and ODP by 43.5% and 29.2%, respectively. These findings further demonstrate the potential of using SS in combination with FA and GGBFS to create high-quality HPC that is both more economical and significantly more sustainable than conventional HPC.