It looks like there is no efficient way of updating (adding and removing) triangles in a polydata-surface in VTK, so for the cutting-simulation I am looking at other visualization options. Despite all the tutorials and documentation out there on the interwebs it always takes about two hours to get these "Hello World" examples running...
Download a zip-file with the source and cmake file: (This compiles and runs on Ubuntu 10.04LTS) qtopengl