Frozen soil masses under various geologic conditions are usually in complex stress states and may carry complex loads with different stress paths. Thus, a comprehensive understanding of the mechanical behaviors of frozen soil under different stress paths is crucial to guide frozen soil engineering and develop the frozen soil mechanics. In this work, triaxial compressive tests under 32 stress paths were conducted on frozen silty clay, taking both global and local strain measurements. The test stress paths were composed of nine initial confining pressures and 14 stress increment direction angles, whose influences on the mechanical behavior were investigated. The coupling effects between them on the strength and deformation characteristics were revealed: the lower the initial confining pressure was, the stronger the effects of the stress increment direction angle on the strength and deformation were, and the larger the stress increment direction angle was, the stronger the effects of the initial confining pressure on the strength and deformation were. This coupling indicated that the influence of the stress path on the stress–strain response might depend on the change of density during loading: the denser the specimen was, the less the anisotropic it was. The uniqueness of the strain increment directions for a certain stress state reached through different stress paths was found, when assuming the direction of the strain rate coincided with that of the stress. An asymmetric failure function in the meridian plane was proposed, and then a three-dimensional strength criterion was constructed by combining the deviatoric-plane failure function of the unified strength criterion. The validity of the proposed criterion was examined by using stress-path test results of three types of frozen geomaterials in the literature.