I'm cutting small squares from a bigger piece of double sided PCB copper clad, with a hand scissors for metal sheets. Alternatively the PCB can be scratched first, then break with pliers along the previously made scratch. Rotary tools are not very good for cutting fiberglass substrate PCB, because fiberglass debris is nasty for lungs if inhaled.
Do NOT use superglue to glue the small squares on top of the copper clad. Cyanoacrylate makes nasty fumes when heated. Instead, solder the small squares of double sided PCB by normal soldering them on top of the copper clad.
Cleaning the copper very well before soldering helps a lot. I'm using the abrasive side of a kitchen sponge (the ones with normal sponge with one abrasive, not metal sponge) and a drop of water. If you don't have that type of kitchen sponge, toothpaste on a piece of cloth works as a fine abrasive, then once the copper is shinny, rinse the PCB with cold water and dry the PCB without wiping it (either with compressed air or by keeping it for a few seconds at 20-50cm in the hot air above a gas stove, or by using a hot air station, etc.).
In case you didn't watch these already:
#123: Build a crystal oscillator from schematic thru prototype construction and testing - DIY
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#122: Electronic Circuit Construction Techniques: review of some prototype circuit building methods
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