To cut a part on the laser cutter’s rotary axis, you need a flat version of your (presumably circular) geometry. You can achieve this by turning your part into a Sheet Metal part and creating an engineering drawing.
Create a thin (1mm or less) cut along the length of your part to make it ‘unwrappable’
Convert the part to Sheet Metal
Switch to the Sheet Metal toolbar tab
Under Create, select Convert to Sheet Metal
Create a flat pattern
Select Create Flat Pattern and the outer surface of the part
In the flat pattern view, create an engineering drawing at 1:1 scale (use a large enough sheet)
Remove the frames, and title blocks
Export the drawing as a PDF
Open the PDF in Inkscape
Remove the centerline
Change the outline’s color to one different from the cuts (blue, for example)
Interrupt large cuts - otherwise, the large off-cut will cam out or fall down, potentially bumping the part. (You can alternately achieve this by using the cropping tool in the laser’s software)