The effective manipulation of perpendicular magnetization through spin-orbit torque (SOT) holds great promise for magnetic memory and spin-logic device. However, field-free SOT switching of perpendicular magnetization remains a challenge for conventional materials with high symmetry. This study elucidates a full electrical manipulation of the perpendicular magnetization in an epitaxial [111]-orientated Pt/Co heterostructure. A large anisotropic epitaxial strain induces a symmetry transition from the ideal C3v to C1v, attributed to the mismatch between [112] and [110] directions. The anisotropic strain also generates a noteworthy in-plane magnetization component along the [112] direction, further breaking magnetic symmetry. Notably, the high-temperature performance under 393 K highlights the robustness of strain-induced in-plane symmetry breaking. Furthermore, eight Boolean logic operations have been demonstrated within a single SOT device. This research presents a method for harnessing epitaxial strain to break in-plane symmetry, which may open a new avenue in practical SOT devices.