In this work, we examine theoretically the cooling dynamics of binary mixtures of spheres and rods. To this end, we introduce a generalized mean field analytical theory, which describes the free cooling behavior of the mixture. The relevant characteristic time scale for the cooling process is derived, depending on the mixture composition and the aspect ratio of the rods. We simulate mixtures of spherocylinders and spheres using a molecular dynamics algorithm implemented on graphics processing unit (GPU) architecture. We systematically study mixtures composed of spheres and rods with several aspect ratios and varying the mixture composition. A homogeneous cooling state, where the time dependence of the system's intensive variables occurs only through a global granular temperature, is identified. We find cooling dynamics in excellent agreement with Haff's law, when using an adequate time scale. Using the scaling properties of the homogeneous cooling dynamics, we estimated numerically the efficiency of the energy interchange between rotational and translational degrees of freedom for collisions between spheres and rods.