The gravity-embedded rock anchorage commonly used in canyon suspension bridges demonstrates that the anti-sliding effect of the tooth-shaped rock mass at the front base effectively enhances anti-sliding stability. This paper relies on the north bank gravity-embedded rock anchorage foundation of Dongtingxi Yuanshui Grand Bridge, comparatively investigates the applicability of two conventional engineering methods strength reduction method and overloading coefficient method in stability evaluation. Results reveal significant differences between these methods in simulated working conditions, mechanical mechanisms, failure modes, and calculation outcomes. Strength reduction method simulates rock strength degradation scenarios. As strength reduction progresses, shear failure zones gradually penetrate the rock foundation, ultimately manifesting sliding instability. The critical strength reduction coefficient represents the anti-sliding stability factor. Overload coefficient method simulates main cable overloading conditions. Under continuously amplified cable tension, the front rock mass experiences extensive compressive-shear failure while the rear rock develops localized tensile-shear failure, exhibiting compressive-shear failure patterns. The critical overload coefficient corresponds to the safety factor of the anti-pull bearing capacity. The physical meanings of anti-sliding stability coefficient and anti-pull bearing capacity safety factor differ significantly, with the latter being notably larger than the former. Both indicators could be adopted simultaneously when required by design specifications, but distinct safety criteria should be applied. For stability assessment of gravity-embedded rock anchorages, the strength reduction method should be prioritized.