This work describes a three-degrees-of-freedom rehabilitation exoskeleton robot for wrist articulation movement: the Biomech-Wrist. The proposed development includes the design requirements based on the biomechanics and anthropometric features of the upper limb, the mechanical design, electronic instrumentation, software design, manufacturing, control algorithm implementation, and the experimental setup to validate the functionality of the system. The design requirements were set to achieve human wrist-like movements: ulnar-radial deviation, flexion-extension, and pronation-supination. Then, the mechanical design considers the human range of motion with proper torques, velocities, and geometry. The manufacturing consists of 3D-printed elements and tubular aluminum sections resulting in lightweight components with modifiable distances. The central aspect of the instrumentation is the actuation system consisting of three brushless motors and a microcontroller for the control implementation. The proposed device was evaluated by considering two control schemes to regulate the trajectory tracking on each joint. The first scheme was the conventional proportional-derivative controller, whereas the second was proposed as a first-order sliding mode. The results show that the Biomech-Wrist exoskeleton can perform trajectory tracking with high precision ( RMSEmax = 0.0556 rad) when implementing the sliding mode controller.