Combining deformation and cutting looks like this. You see a 900 cylinder being dilated slightly, while a number of cuts divides the object into pie-slices. More pictures are over here.
This is a 12x12x12 cube deformed by external forces.
This is the same object, now with a cut. Part of the object deforms, but the result of the deformation does not look realistic. The loose protusion should bend, but instead it appears sheared and stretched. This is the result of the linear-geometry approximation, which is only valid for small deformations. The black dots are mesh-nodes whose position has been fixed.
We perform cuts by changing the mesh to be wherever the scalpel is. You can see how this works in this picture. The original mesh is shown in white.
Here, a cut without node repositioning. A jagged cut surface is the result.
Surface selection. The closest-node heuristic selects a set of faces close to the scalpel sweep
The same object slaughered and ripped by many cuts and many forces.
The last three pictures show off an interesting error (which is also present in the EuroGraphics 2000 paper). The simulation took strain as being G, where G was the gradient of the displacement field. Strain in the linear model really is (G + GT)/2. By leaving out the transpose term, element rotations are disallowed, which can be seen in the pictures as a lack of any bending. It also improved the convergence rates a lot :-)