The quaternion-based classical Terminal Sliding Mode (TSM) control methods tend to induce attitude unwinding problem when directly applied to spacecraft attitude control mission. Moreover, control practice must account for constraints such as actuator output limits and unknown external disturbances. To address these issues, this paper proposes a TSM control method that integrates both anti-unwinding and anti-windup capabilities. The system's kinematic and dynamic models are established based on the unit error quaternion. A new terminal sliding surface is designed, and the finite-time stability and unwinding resistance of the sliding mode are proven using an asymmetric Lyapunov function. Further, a control law with dynamic parameters and an auxiliary system is constructed to ensure finite-time convergence of system states and maintain global unwinding resistance. A nonlinear Disturbance OBserver (DOB) is introduced for dynamic compensation of lumped disturbances, effectively enhancing system robustness. Simulation results show that the method completes the attitude pointing process within 30 s, avoids unwinding, ensures the control torque meets the 0.1 N·m amplitude constraint, and achieves significantly higher control accuracy than traditional methods, providing an innovative solution for high-precision spacecraft attitude control.