For complete utilization of construction and demolition (C&D) waste, an investigation of all size fractions of C&D waste generated during the recycling process should be conducted. In this work, the effects of three recycled concrete materials with different sizes (recycled coarse aggregate (RCA) with a size of 4.75–25 mm, recycled fine aggregate (RFA) of 0.15–4.75 mm, and recycled powder (RP) smaller than 0.15 mm) produced from concrete waste on the fresh and hardened mechanical properties of concrete were evaluated. The replacement ratios of natural coarse and fine aggregates by RCA and RFA were 30, 60, and 100%, and those of ordinary Portland cement for RP were 10, 20, and 30%. The results showed that the concrete properties deteriorated with increasing replacement ratio regardless of the type of recycled materials. The properties were reduced in the order of the use of RFA, RCA, and the simultaneous use of RCA and RFA. In addition, concrete with 30% RP showed lower mechanical strength than concrete with 100% RCA and 100% RFA. However, all concretes could be applicable for structural purposes under different environmental exposure conditions. In particular, concretes with 10% RP and 20% RP showed better cost-benefits compared to natural aggregate concrete with 100% ordinary Portland cement. These promising findings provide valuable initiatives for the effective and complete recycling of C&D waste.