Copper mining, the central axis of Chile's economic development, produces a large number of tailings, which become a potential environmental risk. This study aims to evaluate the mechanical properties resulting from the making of Portland cement mixtures with tailings as aggregates so that they can be eventually used in paving stones for building inactive tailings dams. Tailings coming from two dams at a concentration plant located in Taltal (Chile) were used. Currently, Dam 1 is inactive, while Dam 2 is active. The tailings samples obtained from both dams were granulometrically characterized by sieving. In addition, pH, humidity, Eh, and mineralogical assays (sulfides, oxides, sulfates, carbonates, phosphates, and silicates) were measured. The fines content of the tailings from Dams 1 and 2 with a sieve size of N degrees 200 ASTM were 76.2% and 29.6%, respectively. Therefore, owing to their high percentage of fines, they cannot be as used as concrete aggregates. Aggregates must contain a maximum percentage of fines so that mortars and concrete can meet Chilean standards. In this paper, to comply with a 7% and 15% fines content lower than 0.075 mm, tailings materials were mixed with conventional aggregates containing very little fines. In addition, a reference mixture was made with only tailings aggregates with and without a superplasticizer additive. To measure the mixtures of cement, aggregates, and tailings, bending and compression strength assays were made of the specimens after a 28-day curing, according to the Chilean standard. The results of the study show that the addition of only part of the tailings to the mixture increases bending strength by 26% and compression strength by 180% compared with the reference mortar, with a fines content lower than 0.075 mm in the 7% mixture, thus allowing paving stone manufacture with tailings materials. In addition, it was possible to increase the workability of the reference mixture by using superplasticizers as additives.