Here's a company that makes cookie cutters and how they do it. (I do love seeing how things are made).
But if you'd like to make your own, there are affordable ways to do that. Another benefit is being able to choose your shapes.
She used a disposable metal pan, which had the advantage of providing lots of raw material in lengths long enough for cookie cutters, but I've seen other videos where people cut the top and bottom off of a soda can, cut the remaining rectangle into strips (after cutting the length of the can to produce a flat piece of metal), folded the strips down on one side to reinforce them, and then joined multiple pieces together to create one long strip. (For instructions on how to do that, go to this longer video and go forward to about 4:26 where he connects two strips in a very simple fashion https://www.youtube.com/watch?v=VlX8Vl77G3M ).
I'm not sure if you're a cookie maker, but if you are, happy baking!