This paper studies the deployment control of a spinning hub-spoke tethered satellite formation, which is a challenging issue due to the strong nonlinear coupling between the hub and sub-satellites, and the underactuated nature of the system if no thrust is used for control. The mathematical model of the formation system is established based on the assumption of rigid body of the hub, inextensible tether, and lumped masses of the sub-satellites. Two novel formation deployment controllers are proposed based on tension control and hybrid tension-thrust control strategies, where underactuated sliding mode control and nonsingular terminal sliding mode control method are used, respectively. The adaptive control theory is adopted to estimate the unknown upper bound of the gravitational perturbation caused by the rotation of the system around the hub. It can be proven by the Lyapunov theory that the close-loop systems have bounded and asymptotic stability under these two deployment controllers, respectively. Finally, numerical simulations are conducted to validate the effectiveness and robustness of the proposed controllers.