The first computers were made in discrete parts. At first vacuum tubes, then transistors. Then the first integrated circuits that had only a couple dozen transistors and were based on manually projected stencils. The computers would help a bit, but most of the work was done with pen on paper. What is now done by a single tiny chip was occupying a large board with a hundred integrated circuits - each designed by hand. Never mind precision of the process wouldn't allow more elements in an IC.
At certain point, computers were advanced enough to implement CAD software. This allowed moving the design from paper to circuitry, applying common cut&paste to stuff several chips into one, then plot a large, complex mask on paper to be shrunk by photo-techniques and made into more complex chips. As these entered use, increasingly less of the process was done "by hand" and increasingly more was automated. Specialized software that allowed use of a high-level programming language to "write" the IC architecture, that compiled to paths and transistors without human interaction, robotic assembly lines that could prepare increasingly more complex masks etc.
Think of it that way: you think the mask can't be made using anything less than it produces... are you sure? Can't it be made using something 5% less than it produces? And that one can't be made with something another 5% less complex?
ps. you refer to 'cutting'. That's not how these stencils were made. They were about universally made using photo-etching.
- Make a (big) printout of a layer of the IC.
- Take a photo. Now your printout is the size of a microfiche.
- Spray silicone wafer with conductor, copper vapor or such.
- Spray that with photo-hardening emulsion.
- Shine UV light through the microfiche stencil with optics focusing it to the size of the IC. It hardens the emulsion where paths are to go.
- Apply acid bath, etching the conductor and emulsion away where they aren't needed.
- Wash the emulsion off.
...and so on. Different substances, different emulsions, different masks, layer by layer the chip was built in an entirely analog process. The only digital part was design and plotting of the first stage on huge sheets of paper.