In recent decades, large amounts of construction and demolition waste (CDW) have been generated and accumulated throughout Europe, which is a challenge to manage and control nowadays. This work shows the results of a study carried out with samples of ceramic recycled aggregates (CRAs) and recycled concrete aggregates (RCAs) mixed with cement (C) in mortars. The main objective of this research is to demonstrate how, by adding CRAs and RCAs to a mixture of cement and natural aggregate (NA), it is possible to develop a high-strength mortar and achieve the best mixing ratio. To achieve these objectives, the characterization of the samples was initially carried out such as XRF, XRD and SEM. Next, tests were carried out on the products obtained, such as the consistency of the fresh mortar and the density of the specimens. Finally, a study of mechanical compressive strength was performed at 7, 28 and 200 days. The results show that although both CRAs and RCAs negatively affect the curing process of the specimens, it is possible to develop mortars with compressive strengths greater than 20 MPa. An obvious increase in mechanical compressive strengths was seen between 7 and 200 days of analysis. The results achieved in this research could be an important guide for the management of CDWs by local industries, thus favouring the development of the circular economy.