We present an approach for the automatic generation of patient-specific tetrahedral finite-element (FE) meshes from multiple-label segmented medical images. The approach uses a mesh refinement method with guaranteed tetrahedral element quality and includes a post-processing step with operations to change the mesh topology. Results indicate good approximation of the meshed geometry and acceptable simulation errors for a mechanical problem with a known analytical solution. We also present a method for correcting mesh distortion associated with large-deformation mechanical problems such as those that can arise in dealing with biological soft tissues. This adaptive remehsing scheme is driven by an estimate of the local a posteriori FE error profile. Finally, we demonstrate the use of our approach to carry out a large-deformation simulation of non-infiltrating brain tumor growth starting from a segmented medical image.