This paper shows the results of a study focused on the evolution and properties of mortars made with a mixture of portland cement (PC) and natural mordenite (Mor). To begin, samples of mordenite, cement and sand were studied with X-ray diffraction (XRD), X-ray fluorescence (XRF) and granulometric analysis (GA). Next, mortars with a ratio of 75% PC and 25% mordenite were prepared to determine their initial and final setting times, consistency and density. Continuing, the density, weight and compressive strength of the specimens were determined at 2, 7, 28, 90 and 365 days. Finally, the specimens were studied using SEM, XRD and XRF. The results of the study of the mordenite sample showed a complex constitution where the major mineral component is mordenite, and to a lesser degree smectite (montmorillonite), halloysite, illite, mica, quartz, plagioclase and feldspar, in addition to altered volcanic glass. Tests with fresh cement/mordenite mortar (CMM) showed an initial setting time of 320 min and a final setting time of 420 min, much longer than the 212–310 min of portland cement mortar (PCM). It was established that the consistency of the cement/mordenite mortar (CMM) was greater than that of the PCM. The results of the density study showed that the CMM has a lower density than the PCM. On the other hand, the density of cement/mordenite specimens (CMS) was lower than that of portland cement specimens (PCS). The CMS compressive strength studies showed a significant increase from 18.2 MPa, at 2 days, to 72 MPa, at 365 days, with better strength than PCS at 28 and 365 days, respectively. XRD, XRF and SEM studies conducted on CMS showed a good development of primary and secondary tobermorite, the latter formed at the expense of portlandite; also, ettringite developed normally. This work proves that the partial replacement of PC by mordenite does not have a negative effect on the increase in the mechanical strength of CMS. It indicates that the presence of mordenite inhibits the spontaneous hydration of C3A and controls the anomalous formation of ettringite (Ett). All this, together with the mechanical strength reported, indicates that mordenite has a deep and positive influence on the evolution of the mortar setting and is an efficient pozzolan, meaning it can be used in the manufacture of mortars and highly resistant pozzolanic cement, with low hydration heat, low density, stability in extremely aggressive places and a low impact on the environment.