Abstract: Composite finite elements (CFEs) based on a hexahedral discretization of the simulation domain have recently shown their effectiveness in physically based simulation of deformable bodies with changing topology. In this paper we present an efficient collision detection method for CFE simulation of cuts. Our method exploits the specific characteristics of CFEs, i.e., the fact that the number of simulation degrees of freedom is significantly reduced. We show that this feature not only leads to a faster deformation simulation, but also enables a faster collision detection. To address the non-conforming properties of geometric composition and hexahedral discretization, we propose a topology-aware interpolation approach for the computation of penetration depth. We show that this approach leads to accurate collision detection on complex boundaries. Our results demonstrate that by using our method cutting on high-resolution deformable bodies including collision detection and response can be performed at interactive rates.