The development of sustainable high-performance cementitious concrete with enhanced mechanical properties is essential for improving the performance and reliability of modern urban infrastructure. This study investigates the mechanical performance of cementitious concrete incorporating ground granulated blast-furnace slag, Portland cement, nano-silica, and aluminum sulphate, with particular emphasis on its potential applications in multiscale urban engineering. Nineteen concrete mixtures were prepared using a constant binder content of 530 kg/m³ and a water-to-binder ratio of 0.33. Nano-silica was incorporated at dosages of 10–30 kg/m³ as a partial replacement for GGBS, while aluminum sulphate was added at 4% and 8% of the cement mass. The mechanical performance of the mixtures was evaluated through compressive strength, splitting tensile strength, and flexural strength tests. The experimental results demonstrated substantial improvements in the mechanical performance of the modified concrete compared with the control mixture. The optimum mixture achieved a compressive strength of 63.64 MPa, corresponding to an approximately 41% increase over the control mixture. Furthermore, the splitting tensile and flexural strengths increased by approximately 74% and 77%, respectively, highlighting the potential of the combined modification strategy to improve both load-bearing capacity and resistance to tensile cracking. These improvements demonstrate the potential of incorporating nano-silica and aluminum sulphate into slag–cement-based concrete to develop high-performance materials for demanding urban engineering applications. The findings provide an experimental basis for further development of sustainable cementitious concrete for structural elements, buildings, bridges, and other urban infrastructure where enhanced mechanical performance is a primary design requirement.