Precise control of directional heat flow is essential for advancing applications such as microchip cooling and building thermal regulation. However, existing methods often face challenges related to manufacturing complexity, structural instability, and limited reversibility. Here, we present strain-gradient-induced crystal symmetry breaking as an effective strategy to achieve anisotropic heat conduction. We model a uniaxially bent silicon nanocube and predict an anisotropy ratio of 1.20 at a strain gradient of 0.44%/nm (12% bending strain). This anisotropy arises from two distinct types of strain within the bent lattice: static strain along the axial direction, which significantly impedes heat conduction, and dynamic strain in the transverse directions, which poses a minimal effect on heat flow. The static strain broadens the phonon spectrum and induces phonon overdamping, thereby enhancing scattering and leading to marked reductions in the thermal conductivity. These findings highlight strain-gradient-induced phonon spectrum engineering as a reversible and robust method for directional thermal regulation.