If I were to scale up a twisty puzzle using the scale feature in solidworks, would it still function the same?

I would assume not, because of the tolerance of the puzzle before you scaled it. That's just my opinion, I'm sure it could be incorrect though.

Certain things aren't based on the size of the piece. Screw hole sizes, tolerances between surfaces, fillets, shelling thickness, etc.

Even the tongue/groove between pieces is generally designed to be a specific size (2mm thick for example) regardless of the piece size.

I think the only thing that would prevent the puzzle from functioning though is just the tolerances. They don't scale linearly.

It should work as long as you haven't added tolerances or screwholes yet.

I agree with the above regarding tolerences in principle, but in practice I don't think it will be a problem if you're scaling dimensions by less than 2-fold (since tolerences vary 10-fold from about 0.05 to 0.5mm anyway), as long as you can find screws/fittings scaled in proportion.

There is another reason you don't want to scale a finished puzzle: cost.

If you double the size of a puzzle the cost goes up 8x. If you scale before shelling pieces you can get the cost increase down to as low as 4x.

That's true, but cost will always go up as you scale up, so I guess that was expected, and it wasn't part of the original question which focused on functionality.

Otherwise I agree, shelling after scale-up will avoid costs going up linearly with volume, provided the walls do not become too thin and flexible (more of a problem with larger puzzles).

I guess we're about to find out because I'm waiting for some twisty puzzles that I happened to scale up. I hope for the best.

By what factor did you scale each dimension?

I scaled it all up but 1.5 before shelling.

Then I'm pretty sure you won't have any problems at all. In fact it may even work slightly better than the original, on the basis that any small overhangs will be larger and less likely to pop out given the same amount of force, as long as you've kept the walls thick enough. Also, the "signal to noise" ratio (functional design dimensions vs print resolution) will improve with scale.

Let us know how it works out.