Alan -
If you buy something, you generally have the right to sell the thing you bought. So if you bought an art print you could sell the art print second-hand on eBay. You couldn't make copies of it to sell, but you could sell the thing itself. By extension, you ought to be able to sell the print cut into puzzle pieces. This is, broadly, what's called the "Doctrine of First Use" where the image owner is paid for the primary, or 'first use' of the image but doesn't get a fresh royalty for the same physical object every time it is sold to someone else.
Likewise if you went out and bought a print and said "I want my print glued to plywood and cut into 250 interlocking pieces, Chris, and I'll pay you to do that for me" then again, no law is being broken. You are not hiring me to make a copy of a print. You are hiring me to cut up a print you already own.
However, if I make a digital picture of the print and put it on an Internet site, that's making a copy. So we'd have to be careful how we advertise puzzles.
I think "fair use" comes into play when posting examples of puzzle-cutting to an Internet site for discussion, since it is easy and natural to argue that the image is being used as part of a discussion on the art of crafting puzzles, an educational purpose which is very much in line with the doctrine of "fair use". The puzzle was legitimately made (I cut up an image I had legally bought) and then I photographed my work to fairly illustrate my description of it.
If I was putting a price tag on the image or suggesting that interested buyers contact me privately, that might start to undermine the "fair use" defence and I think if puzzle cutters are posting images on their sites it would be better to rely on an explicit agreement with the image owners concerned.
I am not a lawyer although I've done courses in copyright law in the past as a journalist. So my opinion shouldn't be relied on!