I have never had any luck cutting "soft" substrates, such are rogers duroid. The dielectric material is so soft that the knife dents into it more than cutting.
FR4 boards, being very stiff, can easily be cut. I use an Exacto knife with a stout handle and the big blade.
I cut the area i do not want copper on, then use a soldering iron tip set at very hot to heat up the copper, and it peals away easily. Put the board on a non slip surface so it does not move....i just use my antistatic rubber mat top on the workbench.
Watch your fingers, as you have to put a lot of force on the knife.
To cut FR4 board for prototyping, i use a sheet metal shear:
it is also handy for cutting copper sheet, for forming horns, antennas, emi shields, etc.
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it is going to be a crude circuit, but often that is all you need to do a simple circuit function during a prototype system test. Some random circuits i had lying around:
Note the one with the pre-printed protoboard squares...i use those a LOT for circuits that have plastic packed SMT devices, like amplifiers.
you can get protoboards here:
https://www.busboard.com/SP2-100x100-G
they have 100 x 100 mil pads (the ones i use) or 50 x 50 mil pads