I think you'd have to mock it up for your presentation – print it on a desk-top printer and cut out the cut-out by hand using a scalpel. You'll need to produce a cutter guide for your printer/binder to forme cut the sheet if you then have to print it commercially. Discuss the job with your printer, he may subcontract that part of the finishing.
I think to demonstrate this on screen I'd make one more layer and make a compound shape with a Paper fill and the die-cut holes cut out of it and put it at the top of the stack. Toggle visibility to show closed and open.
Don't forget to delete it before output.
Thank you, Derek and Peter.
Peter, could I ask you to be so kind as to give me step-by-step instructions on how to achieve what you suggestion. Since I will be presenting online, your solution might work best. I want to make sure I understand your process.
Make a new layer and add rectangle to fill the page. Now copy the die-cut shapes you've already created, open the Layers Panel menu and make sure paste remembers layers is NOT checked, select the new layer with the rectangle and Paste in Place.
With the new shapes still selected, hold the Shift key and click the large rectangle you drew to fill the page to add it to the selection. Open the Pathfinder panel and choose the Exclude button in the Pathfinder row (2nd from the right, 2nd row). Fill the new compound shape with [Paper].