Is there an easier way to remove pages from a spiral notebook, without all the mess?
You could try running a blade (knife, scissors, etc) along the spiral binding to make the break more consistent. This will leave the paper withing the small binding portion largely intact.
The problem as I see it, is that the paper tears in different directions. Sometimes an individual ring of the binding will tear through the paper leaving the paper on the full sheet. Other times it tears between two of the binding openings leaving the paper inside of the spiral. Since cutting to the edge of the paper from each individual binding would be tedious and still likely require trimming the final sheet, cutting in the other direction will be quicker and easier.
So you'd cut through all the binding holes leaving a strip within the binding (easily removed in one piece from an end of the binding). The rest of the sheet will need trimming to appear neat, but the result is that there are no small loose pieces to appear messy or linger among the pages/binding of the spiral.
Many spiral notebooks (like the one I use every day) have Perforations all down the side along the spine. However that would still leave you with a 1cm(ish) line of paper remaining down the spiral.
However if you do not want that or your notepad doesn't have the Perforations, you can use a small blade and run it across the holes where the spiral goes through. That would allow you to remove almost all of the page in one go, and then simply pull the paper which is inside the spiral out. That shouldn't make much mess at all since if you cut down every hole, the entire side in the spiral should pull out in one go.
I just cut the pages off of the spiral binding with scissors, maybe 10 pages at a time. The scissor-cut edge of the page may be a little jagged, but for me it never matters.
A similar approach would be to use a utility knife, and just cut through a lot of pages at once. You'll need to draw the utility knife's razor blade along the same cut several times to make it through all the pages.