To investigate the influence of the weak layer dip angle on the creep rupture of the composite rock mass, this paper conducts a graded loading creep experiment on the composite rock mass with different dip angles using the acoustic emission method to examine the fracture evolution process. With increasing load grade, the cumulative total ring count of the rock mass shows a “U”-shaped trend, and the acoustic emission spatial positioning results show that acoustic emission events in the rock mass fracture process are primarily concentrated in the vicinity of the weak layer, while events in other areas are few and dispersed. For rock masses with weak layer dip angles of 0° and 15°, cracks occur in both soft and hard rocks, where shear cracks are dominant in soft rocks, tensile cracks are dominant in hard rocks, and finally, the rock mass mainly exhibits tensile splitting failure. For rock masses with weak layer dip angles of 30° and 45°, most of the cracks exist in the interior of the soft rock, which is dominated by shear cracks. With increasing graded loads, the shear cracks continue to develop along the direction of the weak layer, the upper rock mass keeps slipping and dislocating, and the final failure mode is mainly shear-slip failure. The damage evolution varies with the inclination angle of the weak layer, which can be divided into three stages: initial damage accumulation, damage acceleration, and damage destruction. This demonstrates the ability to predict, prevent, and control the occurrence of creep disasters in rock masses with weak layers.