This study introduces an amphibious spherical robot equipped with a dual-propulsion system (ASR-DPS) and investigates its water-surface motion characteristics. Due to its distinctive spherical geometry, the robot exhibits markedly different hydrodynamic behavior compared to conventional vessels. A comparative analysis of the frontal wetted area is performed, followed by computational fluid dynamics (CFD) simulations to assess water-surface performance. The results indicate that the hemispherical bow increases hydrodynamic resistance and generates large-scale vortex structures as a consequence of intensified flow separation. Although the resistance is higher than that of traditional hulls, the robot’s greater draft and dual-propulsion configuration enhance stability and maneuverability during surface operations. To validate real-world performance, standard maneuvering tests, including circle and zig-zag maneuvers, are conducted to evaluate the effectiveness of the propeller-based propulsion system. The robot achieves a maximum surface speed of 1.2 m/s and a zero turning radius, with a peak yaw rate of 0.54 rad/s under differential thrust. Additionally, experiments on the pendulum-based propulsion system demonstrate a maximum speed of 0.239 m/s with significantly lower energy consumption (220.6 Wh at 60% throttle). A four-degree-of-freedom kinematic and dynamic model is formulated to describe the water-surface motion. To address model uncertainties and external disturbances, two control strategies are proposed: one employing model simplification and the other adaptive control. Simulation results confirm that the adaptive sliding mode controller provides precise surge speed tracking and smooth yaw regulation with near-zero steady-state error, exhibiting superior robustness and reduced chattering compared to the baseline controller.