Shale is a common rock type that is associated with underground engineering projects, and several important factors, such as bedding structure, confining pressure, and the loading and unloading path, significantly influence the anisotropy of shale. Triaxial monotonic loading tests and triaxial incremental cyclic loading and unloading tests of shale under three kinds of confining pressures and five types of bedding inclination angles (θ) were thus performed to investigate the anisotropy of shale in terms of mechanical behavior, acoustic emission (AE), and energy evolution, and reveal the mechanism by which shale anisotropy is weakened. The results show that (1) the compressive strength and elastic modulus of shale decrease and then increase as the θ increases, and that both σ3 and incremental cyclic loading and unloading reduce the anisotropy in terms of the compressive strength and elastic modulus of shale, with the ratio of plastic strain to total strain reaching its maximum at a θ of 60° during each loading and unloading cycle. (2) The failure modes of shale with θ of 0°, 30°, and 90° under triaxial monotonic loading are similar to the counterparts under triaxial incremental cyclic loading and unloading, while the failure modes of shale with θ of 45° and 60° differ significantly under the two loading conditions, and interestingly, the degree to which the bedding plane participates in shale crack evolution under incremental cyclic loading and unloading is considerably lower than that under triaxial monotonic loading. (3) The cumulative AE count and AE b-value of shale first decrease and then increase as the θ increases, while the Felicity ratio decreases as the number of cycles increases. (4) As the θ increases, the total energy density U0 and the parameter m, which reflects the accumulation rate of elastic energy, first decrease and then increase, with both reaching a minimum at a θ of 60°. (5) The mode by which cyclic loading and unloading leads to failure in shale with a θ of 60° is similar to that at a θ of 0° and is the main mechanism by which shale anisotropy weakening occurs as a result of cyclic loading and unloading. The results provide experimental support and a theoretical basis for safer and more efficient underground engineering projects that involve shale.