Throwing is a fundamental skill that enables robots to manipulate objects in ways that extend beyond the reach of their arms. We present a control framework that combines learning and model-based control for prehensile whole-body throwing with legged mobile manipulators. Our framework consists of three components: a nominal tracking policy for the end-effector, a high-frequency residual policy to enhance tracking accuracy, and an optimization-based module to improve end-effector acceleration control. The proposed controller achieved the average of 0.28 m landing error when throwing at targets located 6 m away. Furthermore, in a comparative study with university students, the system achieved a velocity tracking error of 0.398 m/s and a success rate of 56.8%, hitting small targets randomly placed at distances of 3-5 m while throwing at a specified speed of 6 m/s. In contrast, humans have a success rate of only 15.2%. This work provides an early demonstration of prehensile throwing with quantified accuracy on hardware, contributing to progress in dynamic whole-body manipulation.