Live working robots in distribution networks not only reduce the labor intensity of operators but also keep them away from environments with numerous safety hazards. These robots are key equipment for intelligent operation and maintenance in the power maintenance field, and their dexterous manipulation capabilities are crucial for disassembling equipment in complex scenarios. Current research on live working robots in distribution networks primarily focuses on tasks such as lead wire disconnection and reconnection as well as conductor stripping operations, with limited studies on arrester disassembly. During live disassembly of arresters, challenges include insufficient nut positioning accuracy and poor grasping stability. This paper conducts research on planning methods for dual-arm robots to disassemble arresters. First, a grasping strategy integrating YOLOv11-Seg instance segmentation and a centroid-constrained GPD algorithm is proposed. Instance segmentation is used to obtain the arrester mask and centroid coordinates, and a cylindrical range filter is applied to enhance grasping stability. Second, a two-stage visual positioning framework is designed, combining coarse positioning by a global camera and fine positioning by an end-effector camera to achieve millimeter-level nut positioning (median error ≤ 3 mm). An orderly path for nut removal is planned to avoid collision risks. Finally, experiments verify that the proposed method increases the grasping success rate within the centroid-defined range to 85% and controls nut positioning error at the millimeter level. This approach effectively addresses the challenge of disassembling complex structural components during live-line operations, providing an efficient and reliable solution for the dexterous manipulation of distribution network maintenance robots.