It is generally acknowledged that the failure of the layer-crack structure is closely related to rock bursts (a layer-crack structure means a coal or rock rib that is cut by fractures that are parallel or sub-parallel to the surface of the rib). Understanding the mechanical behavior of the layer-crack structure under cyclic loading is beneficial for rock burst mitigation. This study experimentally investigated the influence of the geometry of vertical fissure (i.e., width, length and number) on the mechanical properties of layer-crack rock specimens. The results show that the sensitivity of parameters with respect to the geometry of the fissure from strong to weak is the number, length and width. First, the peak stress under cyclic loading increases by approximately 7.82%–17.35%, thereby exerting an obvious strengthening effect. Second, the fissure geometry slightly affects the energy evolution of the layer-crack specimen, i.e., the input energy density, elastic energy density and dissipated energy density all gradually increase with the increase of the number of cycles. However, when approaching a specimen failure, the increasing rates from quick to slow are the dissipated energy, input energy and elastic energy. Third, the damage variable of the layer-crack specimen shows a concave increasing trend with the increase of the number of cycles. When the number of cycles is equal, the damage increases with the increase of the number of fissures, but it decreases with the increase of the fissure length. Fourth, AE events occur shortly before specimen failures, but rapidly increase near the specimen failures. The accumulated AE events that lead to specimen failures decrease with the increase in the number of fissures. These results can provide some basic data for the research of rock bursts related to the failures of layer-crack structures.