Determine the approximate cut location and lay down a piece of masking tape along the cut. Mark your actual cut-line on the tape and then use a fine tooth blade to cut through the tape and plate together. Peel the tape away from your fresh edge and voila.
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Aequam memento rebus in arduis servare mentem.
Use a diamond bladed saw like a tile saw. They really grind their way through. You didn't mention how fine a finish you wanted but the diamond blade will probably give you what you want. They are now available at most of the major building material supply centers in various diameters, grit sizes and arbor hole sizes. Good luck with your project.
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I'm somewhere between the age of thirty-something and Alzheimer's. I just can't remember where!
All four responses to my inquiry would have worked fine. I have done woodwork projects for over 35 years but never cut graphite plate. I applied self-stick contact paper to both sides of plate, sprayed both sides with contact cement and sandwiched between precut pieces of 1/8" wood veneer. Used fine tooth blade on table saw, all cuts were good without chips and was able to drill perfect holes. Soaked cut pieces of plate in acetone overnight, wood and contact paper removal was no problem.
Fine grained graphite works much like wood. Depends on the power tools you have available as to best method. I would suggest clamping it (gently) to a machine work table on top of a 1/8 to 1/4" thickness of wood. Cut with a slitting saw at medium- high speed and use a vacuum cleaner to control the dust. It is very dirty.
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Do Nothing Simply When a Way Can be Found to Make it Complex and Wonderful
Apply contact paper or laminate film to each side, score each side with glass cutter or carbide scribe, clamp along scribed mark (use strap iron or straight edge) and snap off.
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If death came with a warning there would be a whole lot less of it.