In this study, the fracture initiation−propagation behavior of hydrate-bearing sediment (HBS) of the Shenhu hydrate reservoir in the case of connected reservoir pore water was experimentally studied. First, the effects of hydrate saturation (S H ), clay kinds, and content of montmorillonite on the fracture initiation pressure (p f ), fracture propagation area (R s ), and fractal dimension of the fracture propagation profile (d) were analyzed. Second, the calculation criteria of p f were established. The results showed that the range of p f of the study area was 5.88−9.27 MPa. The effects of S H on the mechanical strength and deformation properties of HBS lead to the p f increase and then decrease with the increase of S H , and the critical S H was 70%. The negative correlation between R s and d determined that the increase of the fracture propagation morphology regularity caused the increase of R s . The presence of clay increased R s and improved the occurrence probability of complex fractures. For the HBS whose tensile strength was less than 0.44 MPa, the Griffith criterion can be used to calculate p f . For the HBS whose tensile strength was higher than 0.44 MPa, the modified von Mises criterion was established by adding the correction term reflecting the increase of HBS brittleness caused by the increase of S H . The absolute and relative error ranges of the established calculation criteria of p f were from 0.03 to 0.84 MPa and from −5.5 to 13.2%, respectively.