This is how I make my jigsaw puzzles, pretty much. You might really appreciate the AI plugin I mention in this post:
It has a table saw tool which is amazing for splitting designs like this. I put a video in the linked post that shows how it works.
And if you are using sheets of material that run to the edge, look in the Free Laser Designs category. I posted a design for crumb tray rulers a few days ago. Just line your material up to the correct spot on the ruler and you’re good.