PHOTH-graphene is a newly predicted 2D carbon material with a low-energy structure. However, its mechanical stability and fracture properties are still elusive. The mechanical stability, elastic, and fracture properties of PHOTH-graphene were investigated using classical molecular dynamics (MD) simulations equipped with REBO potential in this study. The influence of orientation and temperature on mechanical properties was evaluated. Specifically, the Young’s modulus, toughness, and ultimate stress and strain varied by −26.14%, 36.46%, 29.04%, and 25.12%, respectively, when comparing the armchair direction to the zigzag direction. The percentage reduction in ultimate stress, ultimate strain, and toughness of the material in both directions after a temperature increase of 1000 K (from 200 K to 1200 K) ranged from 56.69% to 91.80%, and the Young’s modulus was reduced by 13.63% and 7.25% in both directions, respectively, with Young’s modulus showing lower sensitivity. Defects usually weaken the material’s strength, but adding random point defects in the range of 3% to 5% significantly increases the ultimate strain of the material. Furthermore, hydrogen atom adsorption induces crack expansion to occur earlier, and the crack tip without hydrogen atom adsorption just began to expand when the strain was 0.135, while the crack tip with hydrogen atom adsorption had already undergone significant expansion. This study provides a reference for the possible future practical application of PHOTH-graphene in terms of mechanical properties and fracture failure.