Apply the Edit Normals modifier to the object, select all normals and click on the the Unify button to unify them.

As you can notice, some artifacts appeared on our puzzle piece. To fix this, change the Select By option of the Edit Normals modifier to Face, click on the top face and then on the Break button.

Ok, we just created one piece of a puzzle. But because a whole puzzle is made up of different shaped pieces, we need to create couple more pieces. To do this, just return to the Line in the modifier stack and move the vertices's and if necessary, repeat the bevel and edit normal steps.

After you created couple of different pieces, arrange them in the position they would be in if the puzzle was completely assembled.

Then, create a material with a desired picture in the diffuse slot. Select all of the pieces and apply the material. Next, while all of the pieces are still selected, add the UVW Map modifier to them. Change the length/width in the modifier properties if needed.

Here is what i got when i rendered the puzzle:

Also, a good thing is that you can move the pieces around if you want, and their place in the complete puzzle (picture on the surface) will not change.