Multilayered metallic composites have attracted great interest because of their excellent characteristics. In recent years, the mechanical behavior of Cu/Ti composites is described in terms of macroscopic or mesoscopic scales, but the micromechanism regarding dislocation slip, twinning and shear banding at heterogeneous interfaces remains unclear. In this work, the molecular dynamics method is used to study the uniaxial tensile and plane strain compression deformation of the Cu/Ti multilayered composites with characteristic initial crystal orientations. The simulation results show that under the tensile load, dislocations are preferentially nucleated at the heterogeneous interface between Cu and Ti, and then slip along {111} plane within the Cu layers. The corresponding mechanism is confined layer slip. With the multiplication of dislocations, dislocations interact with each other, and intrinsic stacking faults and deformation twins are formed in Cu layers. However, no dislocation slip or twinning is activated within the Ti layers at this stage of deformation. As the load increases, the stress concentration at the Cu/Ti interface leads to the fracture of the composites. For the composites under plane strain compression, the stress concentration at the Cu/Ti interface triggers the formation of shear bands in the Ti layer, and there are only very limited dislocations within the shear bands and their adjacent area. With the increase of applied strain, the common action of various deformation mechanisms causes the grains to rotate, and the disorder degree of complex atoms increases. In addition, the micro-plastic deformation mechanism and mechanical properties of Cu/Ti complex with different initial orientations and strain rates are significantly different. The results reveal the microscopic deformation mechanism of the laminated composites containing hcp metals.