One of the most important task in surgical simulation is the ability to cut volumetric organs. Several algorithms have lready been described but none of them can actually maintain specific and important topological property of the mesh called manifoldness . In this article we define the notion of manifoldness and we explain why it is important to preserve it. We propose a new algorithm that maintains manifoldness and that implements very simple cut strategy: the removing of soft tissue material, which is an efficient way to simulate the action of an ultrasound cautery. Finally we present experimental results which show the efficiency of this algorithm in a surgery simulation system.