This research work focused on three hot recycled mixtures with optimal proportions of aged bitumen, virgin bitumen, and recycling agent, obtained from a statistics-based Design of Experiments (DoE) framework. To characterize the mechanical response of these three mixtures, the fabricated samples were subjected to a repeated haversine compression test, rut wheel, repeated load creep and recovery, and four-point beam bending test. The mechanical response of these mixtures over a wide range of frequencies and temperatures is assessed with master curve construction. In the case of the creep and recovery test, a three-stage creep curve is analyzed. In the case of the rut wheel test, the rut depth variation and dynamic stability are assessed. In the case of the four point beam bending test, the sequence of fatigue failure is demonstrated by constructing a Lissajous plot variation along with the phase change. The fatigue life is computed by using conventional and energy-based methods. It is observed that the fatigue life of these mixtures is significantly different from each other. The current investigation demonstrated a novel statistics-based DoE framework to obtain optimal proportions of RAP bitumen, virgin bitumen, and rejuvenator. The material characterization reveals that all RAP mixtures are viscoelastic in nature and rate-dependent. The material characterization shows that the material modulus, permanent deformation, and fatigue life are distinct for all mixtures.