In this paper, a model of nanotwinted Cu with [111] texture is constructed, and the anisotropic response mechanism and microscopic deformation mechanism are investigated under shock loading with the impact velocity of 0.5 km/s, 1 km/s, 1.5 km/s and 2.5 km/s from 0°, 45° and 90° loading directions by molecular dynamics simulations. It is found that the textured nanotwinned Cu has obvious anisotropy under 0.5 km/s, 1 km/s and 1.5 km/s, and there are secondary yield and two-stage plastic relaxation under 90° loading. However, the anisotropic response is not obvious under hypervelocity impact (2.5 km/s). Under the shock loading, a large number of intrinsic stacking fault appear, among which the content of 0° and 45° is relatively higher than 90° shock. Under different loading direction, the behavior of multiple twins and dislocation motion varies. Specifically, at 0° loading, multiple twins emit dislocation motion simultaneously, leading to the formation of a large number of faults. At 90° loading, the twin boundary effectively blocks dislocation motion, resulting in less deformation. Under 45° loading, the deformation mode differs from both 0° and 90° loading, causing the original twin boundary to be destroyed and recombined into a new twin lamellar layer with varying thickness. This process creates intrinsic layer faults as well.