This is a quick demo of how to 'cut' convex polygons with texture mapping and still retain the texture mapping. The errors are because I didn't spend any time making sure my convex polygon triangulation was working well.
This uses XNA 4, Farseer Physics 3, and a bunch of custom code. Another, and much better, demo is coming!
http://www.mediafire.com/file/ja1j8t5zps01j2x/TextureCutter.zip