Cutting using a hand fret saw without beveling

[doobie]

I was wondering if there is any secret to cutting hardwood using a hand fret saw without beveling the wood so that I cannot remove the pieces I'm cutting out easily? I'm making a puzzle out of a name with poplar and I just happened to get a nice bevel in both directions on some letters such that I'm having a really hard time getting the piece of wood out. Any suggestions?

Of course I'd love to upgrade to a scroll saw as soon as I decide which one to get...