Topological insulators (TI) can apply highly efficient spin-orbit torque (SOT) and manipulate the magnetization with their unique topological surface states, and their magnetic counterparts, magnetic topological insulators (MTI) offer magnetization without shunting and are one of the highest in SOT efficiency. Here, we demonstrate efficient SOT switching of a hard MTI, V-doped (Bi,Sb)2Te3 (VBST) with a large coercive field that can prevent the influence of an external magnetic field and a small magnetization to minimize stray field. A giant switched anomalous Hall resistance of 9.2 $k\Omega$ is realized, among the largest of all SOT systems. The SOT switching current density can be reduced to $2.8\times10^5 A/cm^2$, and the switching ratio can be enhanced to 60%. Moreover, as the Fermi level is moved away from the Dirac point by both gate and composition tuning, VBST exhibits a transition from edge-state-mediated to surface-state-mediated transport, thus enhancing the SOT effective field to $1.56\pm 0.12 T/ (10^6 A/cm^2)$ and the spin Hall angle to $23.2\pm 1.8$ at 5 K. The findings establish VBST as an extraordinary candidate for energy-efficient magnetic memory devices.