•Fragmentation calculation method for open-pit copper blast muck-piles is proposed.•The new method is based on three-dimensional (3D) laser point cloud data (3D LPCD).•The concavity and convexity features are considered in the new method.•VCCS algorithm is improved to carry out the super-voxel segmentation.•RANSAC algorithm is used to refine segmented fragments during the LCCP clustering. The current calculation methods for the blast fragmentation of muck piles (BFMP) do not consider three-dimensional (3D) feature information, such as concavity and convexity. Thus, their calculation results are inaccurate. In this work, 3D laser scanning technology with high precision, high efficiency, and real-time digitization is used to calculate fragmentation of blast muck piles in open-pit copper mines. The voxel cloud connectivity segmentation (VCCS) algorithm and locally convex connected patches (LCCP) algorithm are used to calculate BFMP from 3D laser point cloud data (3D LPCD). Meanwhile, an improved VCCS algorithm based on discrete features is proposed to solve the segmentation problem of 3D LPCD of small blast muck piles, which cannot be effectively segmented and thus greatly influence the 3D LPCD of large blast muck piles. An improved LCCP algorithm based on plane fitting solves the incorrect segmentation of the surface of large fragments into small pieces of fragments. Dexing Copper Mine, the largest open-pit copper mine in China, is taken as the research object. Results show that the accuracy of the calculation results is about 80% when the fragment sizes are 0.1–0.5 m. Moreover, almost all BFMP can be correctly calculated when the fragment size exceeds 0.5 m.