Splitting a shape that has a contained graphic using existing cut pattern

Hi All,

If I have a shape (similar to the snip below), and I wish to cut it in half using the squiggly line below, I can do it easily using the Virtual Segment Delete Tool.

With the result being shown below (ie. I now have the original shape, cut into 2 pieces, using the sqiggly line as the cut shape):

Now for my question. 

If I have a similar shape but it has a graphic included (see snip below), I cannot use the Virtual Segment Delete Tool, as it does not work on the graphic. In my example, the graphic was an imported SVG file, but I have also tried a PNG file. (The Knife Tool will only cut a straight line). I want a similar result to the above, but with the graphic split over the 2 resulting pieces. 

Thanks for any assistance.