Create a plane that goes across mesh to represent the cross section.
Boolean difference mesh minus plane with the intersection classification option set to "Normal".
Select the edge loop that was just created by the boolean difference.
Modify > Convert > Polygon Edges to Curve.
Alternatively, use the following script to create the cross section at the origin.
After running the script you get a curve!
Get SideFX Labs
Make a geo object
Inside the geo object, make the following:
The geometry you want to make a cross section curve of.
A clip SOP, set "Keep" to "All Primitives"
Next, make a group SOP, where you group edges by bounding box. Make the Y size really small, like 0.0001 small, and the other axis bigger than your bounding box.
Finally, create the Edge Group to Curve SOP, and select the group you made previously.
Alternatively, download the Cross Section HDA