Ignimbrite rock is a volcanic material located in the Arequipa region (Peru), and for centuries, it has been used as a construction material, giving a characteristic light pastel, white to pink color to the city of Arequipa, with white being the most common. In the present study, the potential use of three types of Arequipa raw materials (ignimbrite rock powder, calcined clay powder, and demolition mortar powder) as the main source of new binders or the manufacture of environmentally friendly mortars, without the addition of ordinary Portland cement (OPC) is discussed. In this work, an in-depth characterization of the materials used was carried out. The proposed fabrication route for geopolymeric materials was considered for the manufacture of binders and mortars using an alkaline solution of NaOH with values between 12 and 18 molar, as a trigger for the geopolymerization process. Geopolymeric mortars were obtained by adding a controlled amount of fine sand to the previously prepared mixture of binder raw material and an alkaline solution. Conventional OPC and geopolymeric mortars manufactured under the same conditions were mechanically evaluated by uniaxial compression tests at a constant compression rate of 0.05 mm/min and under normal conditions of temperature and atmosphere, where the most optimal values were obtained for 15 molar alkaline solutions of ignimbrite without the addition of aggregates, with values of compressive strength of 42 MPa and a modulus elastic of 30 GPa. The results revealed a significant increase in the maximum strength and modulus of elasticity values when the volumetric fractions of OPC are completely replaced with geopolymeric binders in the study conditions of this work, demonstrating the enormous potential of the ignimbrite rock and construction waste studied, as raw material of alternative mortar binders without the addition of OPC. With this work, the ignimbrite rock, of great value in the region and also found in other areas of the Earth’s geography, was characterized and valued, in addition to the calcined clay and demolition mortar of the region.