+1 on not using a jigsaw. Too much vibration. Depending on the thickness of the acrylic and the length you wish to 'cut' you may also be able to score it with a sharp object (awl, razor knife) and snap the piece off by clamping it along the scored part. It has to be well clamped/supported when you try this or it won't snap cleanly. You also need to clamp a straightedge to the material while scoring to get a clean line. This will only work for the thinner acrylic, say quarter inch. Not sure I'd try it with half or three quarter.
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