The biological spine of quadrupeds enables sagittal flexion/extension, lateral bending, and axial rotation, playing a crucial role in highly agile and dexterous locomotion. While numerous studies have integrated active spinal joints into quadrupedal robots to enhance agility, most designs simplify control complexity by reducing spinal degrees of freedom (DOF), failing to achieve the spatial tri-axial rotation characteristic of biological spines. Consequently, replicating a multi-DOF biomimetic spine and effectively leveraging it to empower the agile locomotion of quadrupedal robots remains a significant research challenge. In this study, we present S-Cheetah, a quadrupedal robot featuring a 3-DOF bio-inspired serial active spine capable of biomimetic spatial tri-axial rotation. To empower the robot to fully utilize this active spine, we developed a specialized reinforcement learning framework to actively promote the engagement of the introduced spine and maximize the robot's locomotive capabilities by integrating an acceleration curriculum learning strategy with tailored reward functions, such as a gallop gait reward, a spine undulation reward, and a spine steering reward. Experimental results demonstrate that S-Cheetah can achieve a peak speed of 6.9 m/s using the rotary G2 gallop gait and an in-place turning rate of 7.2 rad/s. Besides, the system exhibits an emergent, feline-inspired aerial self-righting capability, allowing it to land stably on four feet from arbitrary orientations during free fall. Finally, through extensive evaluations across diverse locomotion tasks, we prove that the introduction of the proposed 3-DOF spine comprehensively enhances the locomotive agility of quadrupedal robots. Project website: himmy-robotics.github.io/scheetah