This paper employs a dynamic and sliding mesh in the simulation of both uncoupled and coupled surge and roll motions of a tidal stream turbine, utilizing a modified actuator-line method. The modification involves the relocation of blade elements in relation to the grid. Detailed analyses are conducted on the Cp and Cz variations in surge, roll, and coupled motions at various frequencies and amplitudes. It is observed that changing the amplitude and frequency of surge and roll motions both impacts the amplitude of Cp and Cz. Interestingly, the Cp and Cz variations in surge motion are inversely proportional to velocity variations, while they are directly proportional in roll motion. The influence of the surge motion on Cp Cz plays a major role, while the addition of the roll motion increases the mean values of Cp and Cz. Due to the combination of the wake characteristics of both surge and roll, the coupled motion wake exhibits a contraction–expansion oscillation pattern. In a coupled motion with equal periods, the ring and strip tail vortex characteristics of both motions are apparent. A surge period increment diminishes the surge's tail vortex characteristic, whereas an increase in the roll period gradually erodes the roll's tail vortex characteristic. The coefficient variation of the tangential and normal forces (cn, ct) in combined motion mirror that of surge motion, presenting a convex table per surge cycle with depressions at the 1/2T and 1T points. The peak of cn and ct in surge motion are approximately 0.28 and 0.03, respectively, while in roll motion, they are around 0.261 and 0.025. The exploration of cyclic stress impacts on the turbine, and the potential instability on the platform could be valuable directions for future research.