For some work using the Finite Element Method, I manually generated a volumetric 3D mesh with tetrahedral elements, from medical image data. The object has an arbitrary shape that is almost cylindrical. I also have a separate mesh file for only the surface. I am trying to cut a slice / chunk out of the side of my mesh such that I end up with two new meshes that can be aligned at a common interface, and each mesh can function independently (with their own connectivity, etc remaining intact). I need a method that can be reproduced on other meshes of the same kind (some are more fine or more coarse). All the software and computational techniques I have found seem to only work with hollow/surface meshes. Please advice.
P.S. If it matters, the mesh file is in the INRIA MEDIT .mesh format but I have also managed to convert it to a Paraview .vtk format.
P.P.S. I see a vote to close. Please consider the fact that I am working in an interdisciplinary field and this question does not seem to be answered anywhere else. All I need are some pointers.