Abstract: Bedding structure affects the mechanical properties and stability of engineering rock masses. To elucidate the influence of bedding angle on rock deformation and damage process, longitudinal wave velocity tests and uniaxial compression tests were performed on yellow sandstone at bedding angles of 0°, 15°, 30°, 45°, 60°, 75°, and 90°. Furthermore, the influence of the bedding angle on the peak strength, elastic modulus, and failure mode was analyzed. Initial bedding damage and load damage were characterized based on the degradation degree of elastic modulus and evolution characteristics of dissipative energy; moreover, the entire evolution process of coupled layer–load damage was simulated using the logistic function. The influence of the bedding angle on the damage evolution law of yellow sandstone was discussed, and a piecewise constitutive model for simulating the entire deformation process of uniaxial compression was established, combined with the damage mechanics and effective medium theories. The results reveal that with increasing bedding angle, longitudinal wave velocity increases gradually, peak strength and elastic modulus decrease first, then increase, and then decrease, and anisotropy is obvious. The failure mode is closely related to the bedding dip angle. When the dip angle ranges from 0° to 60°, splinter-type tensile failure occurs mainly through the weak side of shear bedding. Moreover, when the dip angle is 75° and 90°, shear slip and splinter tensile failure occur along the weak side of the bedding. The damage evolution curve based on dissipative energy can be divided into four processes: initially undamaged, damage initiation, damage acceleration, and damage deceleration termination. A theoretical damage model constructed using the logistic function can effectively simulate and predict the entire damage evolution process. The ratio of maximum value to minimum value of initial bedding damage is approximately 1.41, indicating that bedding angle substantially affects the initial damage. The piecewise constitutive model can describe the entire stress–strain process of layered yellow sandstone under uniaxial compression, and the theoretical model curves agree well with experimental data. Parameters a and r represent the initial damage degree and damage evolution rate, respectively. Larger a values typically correspond to a lower initial damage degree and higher peak strength. The larger r is, the faster the damage variable develops and the greater the maximum damage evolution rate is. Thus, the theoretical curve shape of the constructed constitutive model is determined by parameters a and r.