Reliable anchoring of slip is essential for preventing axial slippage of pipeline plugging robots under high-pressure plugging conditions. However, excessive tooth penetration may induce furrow formation, local plastic deformation, and hard-contact damage on the inner wall of the pipeline. To balance anchoring capacity and pipe-wall protection, this study establishes a mechanical model for the slip–pipe interaction and analyzes the effects of key structural parameters on slip anchoring performance. The self-locking condition between the slip and slip bowl is first derived, and the minimum equivalent friction coefficient required for stable anchoring is determined. Subsequently, an explicit finite element model of the slip anchoring process is developed to evaluate the influence of bevel angle, tooth profile angle, and curvature radius on the von Mises stress and equivalent plastic strain of both the slip and the pipe wall. Based on the simulation results, an orthogonal parameter optimization scheme is conducted to identify the optimal structural combination. The results show that the optimized slip structure, consisting of a 20° bevel angle, a 90° tooth profile angle, and a 150 mm curvature radius, can effectively reduce pipe-wall damage while maintaining reliable anchoring performance. This study provides a theoretical and numerical basis for the structural design and optimization of anchoring slip in pipeline plugging robots.