This paper proposes an efficient method for removing tetrahedra from a tetrahedral mesh while keeping its manifold property. We first define precisely the notion of manifold tetrahedral mesh and stress its relevance in the context of real-time surgery simulation. We then provide a method for removing a tetrahedron that complies with the manifold definition. This removal may require in some cases the removal of neighboring tetrahedra. After providing an exhaustive description of the tetrahedron removal algorithm, its efficiency is evaluated for different mesh configurations. This algorithm is currently used in the context of real-time surgery simulation where the action of an ultrasonic lancet can be simulated by the removal of small set of tetrahedra from a tetrahedralisation.