Virtual cutting of deformable objects is at the core of many applications in interactive simulation and especially in computational medicine. The ability to simulate surgical cuts, soft tissue tearing or fractures, is essential for augmenting the capabilities of existing or future simulation systems. In this thesis, we present a new remeshing algorithm based on the finite element method. For tetrahedral elements with linear shape functions, we combined remeshing algorithm with the movement of the nodes to the cutting surface, called snapping in the literature. Our approach shows benefits when evaluating the impact of cuts on the number of nodes and the numerical quality of the mesh. When applying our remeshing algorithm to quadratic shape functions, we observe similar results. Due to the curved surfaces of the elements, when using quadratic shape functions, the snapping of nodes entails higher challenges. Thus, to investigate into the snapping, experience has been gathered on triangular shell elements, simulating fractures. Beyond the simulation of fractures, our remeshing approach for tetrahedral elements is generic enough to support a large variety of applications. In this work, we are the first to present results on the detection of topological changes, such as fractures, tearing and cutting, from a monocular video stream. Ex amples with highly elastic silicone bands, in-vivo livers and ex-vivo kidneys show the robustness of our detection algorithm, which is combined with the remeshing approach, in different scenarios. Finally, the augmentation of internal organ structures highlights the clinical potential and importance of the conducted work.