Wiping down a tool or wiping up a mess with a small rag and then throwing it out simplifies cleanup:
Long ago, I applied scissors to old towels / t-shirts / whatever to get randomly sized squares, but when Mary began using rotary cutters for her sewing projects I immediately saw the light. A few times a year, I lower the scrap box level and restock the shop wipes boxes.
A laser cutter is even better:
Flatten the rag on the honeycomb, drag a few rectangles into place, and fire the laser:
Something like 50 mm/s at 60% power works for all the fabrics I’ve tried, from worn-out towels and dead sweatpants to napkins and t-shirts. Thinner fabrics can be stacked, but wrinkles and seams get in the way of clean cuts.
Rounded-corner rectangles are easy enough to draw and the scrap cloths have different shapes, so I don’t see much point in saving a file with any specific layout. Your scrap box may be more orderly.
A clean cut lets the outer cloth just lift away:
The wipes give off a distinct smell of charred cloth, but running them through the clothes washer in a big mesh bag with everything else solves that problem.
Obviously, one couldn’t possibly justify a laser cutter to make shop wipes, but if you happen to have one just standing around, well …
The Smell of Molten Projects in the Morning 
Might Mary consider using the laser cutter for cutting patterns?
I’m inching my way toward that goal, but the accuracy / alignment / positioning requirements turn out to be much more complex than I imagined.
Also, laying out known-good fabric atop a crusty honeycomb platform is, as they say, a nonstarter.
Just be careful where you throw them away if you wipe down a machine or anything else oily. https://www.essexct.gov/fire-marshal/bulletins/rise-in-fires-due-to-improper-disposal-of-oily-rags
Aye!
The big red fireproof oily waste foot-pedal-flip-top shop trash can went with the rest of the shop stuff, much to my continuing regret.
Nowadays, I immediately march oily and solvent-wet raglets to the outdoor garbage can and drape them over the contents, where I figure the cloth gets plenty of breathing / cooling room and the solvent vapors stun the bugs.
So far, so good …