Construction and demolition waste accounts for a significant amount of the total solid waste produced worldwide, and its recycling is challenging. Although some demolition waste is processed into recycled sand and rubble, the finer fractions resulting from screening and washing of recycled aggregates are not used. This research investigates the potential of use of real demolition wastes, namely concrete screening fines (CS), mixed concrete-ceramic screening fines (MS), and mud from recycled aggregates washing (WM), as supplementary cementitious materials (SCMs) in eco-efficient blended cement. The study employed various experimental methods, such as isothermal calorimetry, thermogravimetric analysis (TGA), and setting time tests, to evaluate the hydraulic activity of waste materials and the Chapelle test and TGA to assess their pozzolanic activity. The mechanical properties and microstructure of mortars containing 20% of waste powders were evaluated using compressive strength tests and scanning electron microscopy (SEM). The results showed that thermal treatment of waste materials at 500 °C improved the mechanical properties of mortars, increasing Strength Activity Index (SAI) by 10% for CS and MS and by 6% for WM after 90 days of curing. All three waste types achieved similar mechanical properties, with compressive strengths of at least 37.93 MPa, 46.25 MPa, and 51.33 MPa after 7, 28, and 90 days of curing, respectively. The contribution of waste powders to mortar strength was due to filler effect and partially dehydrated C-S-H products. However, pozzolanic ceramic inclusions in waste powders did not affect mortar strength at a 20% substitution rate. Therefore, the research findings indicate that waste materials derived from demolition can potentially be used as environmentally friendly materials in construction. Their use as SCMs with a substitution rate of 20% can reduce the CO2 emissions of cement production by at least 10.7%.