Add you vector to the canvas.

Add 2 5mm wide rectangles that are taller than the vector and place them roughly where you want them.

Group the 2 rectangles together, select it with the animal, and horizontally center to make a more accurate placement.

Subtract the rectangle from the original image.

Add rectangles around each of the 3 parts.  They can be the same height or you can vary them for some added interest.

Outline each of the rectangles.

Move all 3 outlines to the back.  Subtract the inner rectangles from the outer rectangles.

Select the new outline with the inner piece and combine them.  Do this for all 3 sets.

Arrange the parts on your canvas for optimal cutting.  

I used a large sheet so that my final piece is about 12" tall.

Cut this out of 3mm basswood plywood using the default settings (100 power/35 speed).

Use a couple different colors (or more!) and randomly spray paint the design.

Let this dry.

As it dries you can adjust by adding more layers until you like the final appearance.

The final creation can be hung on a wall with command strips (I cut them into thinner parts so they don't show).