Healing outcomes of periodontal and implant-related regenerative procedures are closely related to wound stability, which is partially determined by biomechanical properties and behaviors of oral mucosal tissues. Studies on soft tissue behavior under biomechanical forces in oral regeneration models are scarce. Thus, this review aims to (1) contrast the microstructural differences between the attached gingiva (AM) and lining (LM) mucosa; (2) evaluate biomechanical behaviors of the two mucosal types; and (3) relate residual flap tension to the prevalence of wound opening after regenerative procedures. Compositional and structural differences between the AM and LM explain their biomechanical property differences. Wound destabilizers, including tissue recoil stemming from its viscoelastic property, muscle pull, and inflammatory edema (created after the flap-releasing procedure for primary wound closure) interfere with wound stability. Residual flap tension < 0.05 N is a prerequisite for sustained wound closure. Tissues under stress can exert negative cellular changes, resulting in necrosis and wound dehiscence. Biomechanical properties and the variations between AM and LM dictate the degree of wound stability. Efforts should be made to reduce the negative impact of the potential destabilizers to optimize wound stability.