I had the exact same issue when I first started PPing. First I switched to vellum and was much happier because it tears easier. Then I switched techniques and now I use the fold-and-stitch method - no ripping! Instead of stitching the line on the paper, fold the paper on that line and stitch right next to it. Trim with an add-a-quarter ruler and you're done. Vellum works great for this technique because you can see through it, so you can see if you're folding on the line.