The structural and electronic properties of the 1T-SnS2/MoTe2 heterostructure were investigated based on density functional theory and Berry curvature calculations. Considering the strong spin-orbit coupling and space inversion asymmetry, large Rashba spin splitting of electronic bands appeared in this hybrid system. The Rashba coupling parameter αR in 1T-SnS2/MoTe2 reached 0.383 eV Å. Importantly, αR can be effectively tuned by biaxial strain. Moreover, our first-principles calculations show that the 1T-SnS2/MoTe2 heterostructure possesses a high carrier mobility of 5038.46 cm2 V-1 s-1. The Berry curvature and spin splitting were opposite at the K and K' valleys. Hence, the valleys and spins were simultaneously locked and polarized, and the valley and spin Hall effects simultaneously occurred.