This paper proposes a novel method for a real-time cutting simulation of deformable objects using meshless method. The method utilizes a rapid refinement of topological relations among the simulation nodes of meshless deformable objects. Topological relations are defined as an undirected graph based on a visibility criterion. The graph connects the adjacent nodes that lie within a support of each node. The topological relations are refined by removing the edges of the graph that is intersected by the cut surface during the cutting simulation. Our approach utilizes a bounding volume hierarchy (BVH) to accelerate the computation of the intersection test. The BVH reconstruction algorithm is proposed to account for the cases where pieces of the object are completely cut out from the object. Algorithms to examine the connectivity among simulation nodes and accordingly reconstructing the BVH using two-level BVH are presented. The proposed approach achieves real-time cutting simulation of deformable objects through the rapid refinement of the topological relation. In addition, the computational performance of the cutting procedure is preserved during the entire simulation, thanks to the real-time reconstruction of the BVH. Copyright (c) 2012 John Wiley & Sons, Ltd.