The massive growth of the construction sector has increased demand for sustainable concrete that meets the requirements of modern eco-friendly policies; this in turn has made it necessary to reuse abundant and recycled materials to achieve this end. In this study, crushed clay brick (CCB) as a coarse aggregate and dune sand (DS) as a fine aggregate were used to produce a sustainable concrete. An experimental programme was accomplished by performing partial replacement by DS of conventional sand (CS) at various percentages (25%, 35%, and 50%), with a similar procedure used for crushed clay brick (CCB) and conventional coarse aggregate (CA). The impact of this dual aggregate replacement on workability, density, tensile splitting, and compressive strength was then studied, and the experimental results showed that the density decreased by 12.3% as the dual replacement of aggregates increased to 50%. The workability of the sustainable concrete was within the standard limits, while the results of the slump tests ranged between 120 mm for control concrete and 80 mm as the dual replacement of aggregates increased to 50%. Both the splitting and compressive strengths of the produced concretes were systematically decreased as the dual replacement of aggregates increased under 7- and 28-days curing. The produced concrete was thus deemed to be generally affordable though suitable only for general small works or non-structural uses.