Here's one way to do what you want...
1) Place the Deer on the board
2) Draw the area shape that the head sits on and let the antlers overhang, as you wish
3) Make the area shape a Carve Region of a suitable depth
(so the deer head looks ok, yet still leaves ample thickness for the underlayment)
4) Select both the region and the deer, then click the Outline tool
5) Make the outline a Cut Path