Thanks for your feedback. This is a very good idea, and is something we considered putting in for version 2 but in the end had to drop it due to time constraints on the project. Essentially we wanted to be able to make sure all the core functionality worked really well and as many bugs as possible were ironed out when we released it. However, we'd certainly consider again including it in any future version of the product.
For now as a workaround I'd suggest the following once you've created your diagram and are happy with it. Under the File menu select Export > Image. Then, in the dialog that appears, under "Save as type:" select "Enhanced Metafiles (*.emf)", then assign a filename and click Save. This will save your diagram in the metafile vector format which is obviously much more space efficient than PNG.
You can now import the EMF into another application for printing. I've not tried Visio, although I'd imagine this will work quite well. What also works really well is a spreadsheet application. I've used Excel for this, but I imagine it would also work fine with OpenOffice.org Calc. The only thing you have to watch is that these diagrams can use a lot of paper: I had one the other day that if I'd printed it out would have taken over 3000 sheets of A4 paper. We could have quite literally wallpapered the office with it!
Anyway, hope that helps you out and thanks again for the feedback.