I'm not sure how the pieces themselves are created ( i.e., number of pieces and their shapes ). But, a die needs to be created in order to cut the pieces out of a thick card stock. The picture itself is, obviously, a photograph that is printed on a coated sheet and laminated to the card stock. So, the puzzle itself can be a layered Illustrator file with a Placed photograph. Your die cut stamp needs to be on a separate layer. Like that, see?
We are puzzled.