Cut Out Paper Puzzles
Use sturdy paper for cutting out your jigsaw puzzle. Photographs work well. With printers, you can print images on cardstock paper as well as photograph paper. For a really large paper puzzle, you would need to go to a print shop and have them print the image off of their roller paper.
To turn your printed image into a puzzle, flip it over. On the back side, using a pencil, mark up the blank side in a grid. Draw the grid the rough size you want all the pieces. A basic puzzle piece is squarish (or in a slight rectangle shape) with rounded knobs and niches on each of the sides. Unless the side is an edge, in which case it's flat. On your pencil-marked grid, add in rounded knobs along the sides. On the piece that gets a knob, it's connecting neighbor got a niche. To help with cutting out, be sure to erase the part of the grid line where you put in a knob so you don't accidentally cut straight. Look at the pieces of a puzzle for ideas.
Now that you have your paper marked out. Cut out the pieces, following the lines. Depending on the size of the puzzle pieces, cutting out may be challenging. Smaller pieces will take a more careful hand. A small pair of scissors might be able to make the tight turns around the bases of the knobs. If not, lay the picture on heavy cardboard, or other cutting surface, and use an exacto-knife. Again, cut carefully so you don't cut yourself. If you are not used to handling an exacto-knife, either get adult help (if you are young) or practice using the knife on simpler cuts first.
Another option to consider, to make your puzzle sturdier, is to first cover the image side with clear contact paper before marking the grid and cutting. The clear contact paper will make the puzzle pieces stronger and tear-resistant, but will also make cutting them out a little more difficult.
You can also make your paper puzzle sturdier by first gluing the image to cardboard or even foam board. If so, glue the image and smooth it flat. Give it plenty of time to dry, say overnight, before marking it up and cutting out the pieces. Again, adding cardboard will make your puzzle stronger, but also harder to cut out. Use a sharp exacto-knife.