Mine punched right through the sticky pages, no jamming, sticking etc. so Im not sure how to help with that problem. You can however, use the Ornament Movers and Shaper die cut (the small piece) to cut ornaments from your sticky pages.
here is the sandwich for your big shot: cutting plate, sticky pages, movers ornament piece, cutting plate, hard plastic black texturz impressions pad.
Someone mentioned that their punch got sticky. Mine did not... and I cut about 20 of these. But when my scissors get gunk-y (like from sticky strip) I clean them with a baby wipe. the alcohol in the wipe breaks down the gooey stuff. try cleaning your punch, then foil & wax paper to sharpen & un stick
Hope this helps...