If you can, saw it as close to a circle as possible first. If it is later going to be drilled (for tubes etc) then drill these holes first if they might help you to grip it (e.g. using screws into a wooden faceplate). IanT's approach sounds good, might be safer if you use double-sided tape or superglue to hold the centre portion in place so it doesn't spring off the lathe as you cut through.
I cut a 4 inch circle out of 1/8 aluminium by making a trepanning tool adaptation of my big boring head, then using it on my mill, clamping the ali on a bit of MDF with strap clamps. As ali is similarly "grabby" to copper this might also work (also indicates that it would work on the lathe faceplate).