Understanding the effect of clay on the mechanical properties and strength criteria of hydrate-bearing sediments (HBS) is essential for evaluating the safety of clay-rich reservoirs. In this study, a series of triaxial shear tests were conducted to investigate the impacts of clay type and content on the mechanical behavior of I-HBS (hydrate-bearing sediments containing illite) and M-HBS (hydrate-bearing sediments containing montmorillonite). The findings reveal that M-HBS exhibit greater susceptibility to strain hardening compared to I-HBS, accompanied by more extensive volume deformation, and both strain hardening and shear shrinkage intensify with increasing clay content. Moreover, the results demonstrate higher failure strength and Young's modulus in I-HBS than M-HBS. The failure strength of sediments is affected by both the clay content and effective confining pressure, with an established relationship between the failure strength and these two factors. Additionally, the cohesion and internal friction angle of sediments exhibit distinct linear correlations with clay content due to variations in the clay type. The Mohr−Coulomb strength criterion incorporating the clay content is established, enabling the prediction of shear strength in clay-rich hydrate reservoirs. The clay type and content are the cause for different strengths and shear mechanisms of sediments. This research holds significant implications for the safe mining of natural gas clay-rich hydrate reservoirs.