Ha. OK. This is a bug in how I handle non-triangle polygons.
Basically for a polygon I render a set of triangles, which are generated by picking one vertex and generating triangles in a loop to all the other vertices (called a triangle fan)
So, if you export the file, you will see that it is fine. It just looks broken.
But, if you try a cut-paste operation it will fail, because that also depends on the triangles of the polygon.
So, I will need to figure out a better tessellator =).
But in general, meshmixer will not work very will with such low-poly models and highly non-convex faces. It is very hard to do the kinds of things that meshmixer does without a decent sampling of the surface...the only alternative would be to insert edges into your faces, which is very hard to get right...