To address the challenge of reusing hardware logic in the implementation of a multi-axis stepper motor controller, which leads to excessive consumption of logic resources, a time-division multiplexing strategy grounded in a speed curve algorithm has been proposed. Initially, leveraging the kinematic theory of rigid bodies rotating about a fixed axis alongside the control principles of stepper motors, a mapping relationship between the pulse period of stepper motor control and the corresponding kinematic physical quantities is established. Subsequently, the two rotational modes of uniform acceleration and uniform deceleration are integrated with the pulse calculation formula, optimizing the velocity curve calculation method. Building upon single-axis non-time-division multiplexing control, the design of the time-division multiplexing multi-axis velocity curve algorithm is executed by fully utilizing the time intervals of control pulse outputs. Ultimately, the IP core for the time-division multiplexing controller of the two-axis stepper motor is developed, achieving a 33.68% reduction in logic resource usage and 14.04% reduction in thermal power consumption compared to the two-axis non-time-division multiplexing IP core. A hardware experimental platform is constructed to validate the algorithm, with results indicating that the time-division multiplexing IP core enables precise control of the two-axis stepper motor, maintaining an angular displacement following error within ±8 steps (±0.9°).