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I have just spent a good part of the day cutting out 3/16" acrylic letters. I have tried different blades in the bandsaw, different blades in the jigsaw. All have needed sanding of the edges after the cut.
This is what worked best:
I have cut a 3 mil vinyl template of the letters and stuck it to the face of the acrylic. Then I smear a good coat of motor oil over the letter. Cut it out on the scroll saw and no sanding required!!