In the view of the recycling and upscaling processes of waste materials, three different precursors, namely metakaolin, fly ash and volcanic ash, were mixed with Na- or K-silicate to produce binders aimed for the synthesis of geopolymer mortars based on construction and demolition wastes (CDWs). These later, used as aggregates in amount of 50 wt.%, were sampled in two geologically different Italian areas. A comparative study was carried out through a multidisciplinary approach using mineralogical–chemical analyses and physical–mechanical tests for the characterization of six binders and twelve mortars. The aim was to verify the effects of CDW interactions on binders as well as the extent of their compositional influences on the final properties. The chemical and mineralogical results evidenced strong compositional differences among the CDWs, differently influencing the physical–mechanical performances (i.e., compressive strength, density, water absorption and porosity) of the mortar samples. Regardless of the types of precursors and CDWs used, a better influence of K-silicate than sodium on the synthetised samples was observed. Furthermore, the higher versatility of metakaolin mortars with any type of CDW used was noted. Contrary, fly ash and volcanic ash mortars showed better properties with CDWs based on their high silica content and volcanic minerals. The study highlighted the critical roles of the CDW composition and precursor selection in mortar production. It confirmed that CDWs can be recycled for geopolymeric synthesis through proper characterisation and binder selection. Optimising these parameters allows for the successful integration of CDWs into geopolymeric materials. This process supports the advancement of a circular economy in the construction industry.