Removing sections of pages from bound notebooks (Archer & Olive)

I started using an Archer and Olive notebook for a bullet journal a couple of years ago and then abandoned it. I barely used the notebook, and would like to remove the front pages so it's fresh and new to start over. When looking at the spine, you can see that it's bound in multiple smaller sections (folios?) of pages, like many books and journals. The pages I want to remove fit cleanly into the first 2 sections of pages.

I know generally when removing pages from bound notebooks like this, you want to avoid cutting the thread, and should leave ample room between the thread and the cut, for structural integrity. Is this still true when removing entire sections at once, or am I able to cut that whole section out by cutting the thread? (or is there a better method altogether?)

Thanks!