Recently, a dysregulation of the Hippo-YAP/TAZ pathway has been correlated with intervertebral disc (IVD) degeneration (IDD), as it plays a key role in cell survival, tissue regeneration, and mechanical stress. We aimed to investigate the influence of different mechanical loading regimes, i.e., under compression and torsion, on the induction and progression of IDD and its association with the Hippo-YAP/TAZ pathway. Therefore, bovine IVDs were assigned to one of four different static or complex dynamic loading regimes: (i) static, (ii) “low-stress”, (iii) “intermediate-stress”, and (iv) “high-stress” regime using a bioreactor. After one week of loading, a significant loss of relative IVD height was observed in the intermediate- and high-stress regimes. Furthermore, the high-stress regime showed a significantly lower cell viability and a significant decrease in glycosaminoglycan content in the tissue. Finally, the mechanosensitive gene CILP was significantly downregulated overall, and the Hippo-pathway gene MST1 was significantly upregulated in the high-stress regime. This study demonstrates that excessive torsion combined with compression leads to key features of IDD. However, the results indicated no clear correlation between the degree of IDD and a subsequent inactivation of the Hippo-YAP/TAZ pathway as a means of regenerating the IVD.