It is known that the quantum mechanical ground state of a nanoscale junction has a significant impact on its electrical transport properties. This becomes particularly important in transistors consisting of a single molecule. Because of strong electron-electron interactions and the possibility of accessing ground states with high spins, these systems are eligible hosts of a current-blockade phenomenon called a ground-state spin blockade. This effect arises from the inability of a charge carrier to account for the spin difference required to enter the junction, as that process would violate the spin selection rules. Here, we present a direct experimental demonstration of a ground-state spin blockade in a high-spin single-molecule transistor. The measured transport characteristics of this device exhibit a complete suppression of resonant transport due to a ground-state spin difference of 3/2 between subsequent charge states. Strikingly, the blockade can be reversibly lifted by driving the system through a magnetic ground-state transition in one charge state, using the tunability offered by both magnetic and electric fields.