@EmilioPisanty It's a bit hard to answer without knowing how you would like to specify these lines. In any case, you can build a mesh like this: ToElementMesh["Coordinates" -> {{0.1, 0.2, 0.3}, ...}, "MeshElements" -> {TriangleElement[...], ...}] (cf. GraphicsComplex). Consequently, what you can do is look at mesh["Coordinates"] and mesh["MeshElements"] and filter out the elements that you want to keep and then reconstruct the mesh.