Lightweight cement mortars containing end-of-life tire rubber (TR) as aggregate were prepared and characterized by rheological, thermal, mechanical, microstructural, and wetting tests. The mixtures were obtained after total replacement of the conventional sand aggregate with untreated TR with different grain sizes (0–2 mm and 2–4 mm) and distributions (25%, 32%, and 40% by weight). The mortars showed lower thermal conductivities (≈90%) with respect to the sand reference due to the differences in the conductivities of the two phases associated with the low density of the aggregates and, to a minor extent, to the lack of adhesion of tire to the cement paste (evidenced by microstructural detection). In this respect, a decrease of the thermal conductivities was observed with the increase of the TR weight percentage together with a decrease of fluidity of the fresh mixture and a decrease of the mechanical strengths. The addition of expanded perlite (P, 0–1 mm grain size) to the mixture allowed us to obtain mortars with an improvement of the mechanical strengths and negligible modification of the thermal properties. Moreover, in this case, a decrease of the thermal conductivities was observed with the increase of the P/TR dosage together with a decrease of fluidity and of the mechanical strengths. TR mortars showed discrete cracks after failure without separation of the two parts of the specimens, and similar results were observed in the case of the perlite/TR samples thanks to the rubber particles bridging the crack faces. The super-elastic properties of the specimens were also observed in the impact compression tests in which the best performances of the tire and P/TR composites were evidenced by a deep groove before complete failure. Moreover, these mortars showed very low water penetration through the surface and also through the bulk of the samples thanks to the hydrophobic nature of the end-of-life aggregate, which makes these environmentally sustainable materials suitable for indoor and outdoor elements.