The microgravity environment on asteroids necessitates the inclusion of anchoring devices on asteroid probes to facilitate in-situ landing detection. Complicated working conditions faced by asteroid probes significantly increase the difficulty of the anchoring device’s task. In this paper, based on the discrete element method (DEM), the anchorage performance of a triple-drill anchoring device under different external forces and drilling depth combinations is investigated. The forces on the probe and landing legs and the damaged area of the particle domains are analyzed to obtain the influence of the external force direction on the anchorage performance. Five drilling depth combinations are selected to represent the complicated working conditions asteroid probes face. Then the ultimate anchoring forces of the five drilling depth combinations under the different external force directions are calculated and analyzed. This work reveals the anchorage mechanism under complex working conditions and provides a reference for asteroid exploration missions.