Development of dexterous robotic joints is essential for advancing manipulation capabilities in robotic systems. This paper presents the design and implementation of a tendon-driven robotic wrist joint together with an efficient Sliding Mode Controller (SMC) for precise motion control. The wrist mechanism is modeled using a Timoshenko-based approach to accurately capture its kinematic and dynamic properties, which serve as the foundation for tendon force calculations within the controller. The proposed SMC is designed to deliver fast dynamic response and computational efficiency, enabling accurate trajectory tracking under varying operating conditions. The effectiveness of the controller is validated through comparative analyses with existing controllers for similar wrist mechanisms. The proposed SMC demonstrates superior performance in both simulation and experimental studies. The Root Mean Square Error (RMSE) in simulation is approximately 1.67e-2 radians, while experimental validation yields an error of 0.2 radians. Additionally, the controller achieves a settling time of less than 3 seconds and a steady-state error below 1e-1 radians, consistently observed across both simulation and experimental evaluations. Comparative analyses confirm that the developed SMC surpasses alternative control strategies in motion accuracy, rapid convergence, and steady-state precision. This work establishes a foundation for future exploration of tendon-driven wrist mechanisms and control strategies in robotic applications.