Open the image.
Add a new layer, with a white background. 
Set mode of this layer to "multiply".
Filters->Render->Pattern->Jigsaw.
Set number of pieces wide, number high. Set Bevel Width to 0.
Save the "complete" puzzle.
Select the magic select tool
Select the puzzle layer.
Select a puzzle piece.
Select the background layer.
Cut the selection from the Background layer.
Save the image.