The use of waste materials as alternative aggregates in cementitious mixtures is one of the most investigated practices to enhance eco-sustainability in the civil and construction sectors. For specific applications, these secondary raw materials can ensure adequate technological performance, minimizing the exploitation of natural resources and encouraging the circular disposal of industrial or municipal waste. Aiming to design and develop lightweight paving blocks for pedestrian or very light-traffic purposes (parking area, garage, sidewalk, or sports surfaces), this paper presents the material characterization of rubberized cement mortars using ground waste tire rubber (0–1 mm rubber powder and 1–3 mm rubber granules) to totally replace the mineral aggregates. Considering recommended requirements for concrete paving members in terms of mechanical strength, water drainage performance, acoustic attenuation, and dynamic and energy absorption behavior, a comprehensive laboratory testing is proposed for five different formulations varying the sand-rubber replacement level and the proportion ratio between the two rubber fractions. Tests highlighted positive and promising results to convert laboratory samples into pre-cast members. The “hot” finding of the work was to prove the feasibility of obtaining totally rubberized mortars (0 v/v% of sand) with suitable engineering performance and enhanced eco-friendly features.