PRIMER 22.1
Cutting Through 3D (Solid and Thick Shell) Elements
Cutting Through 3D (Solid and Thick Shell) Elements

This is simple: the polygon generated where the plane intersects the element is used unconditionally. It will have between 3 and 6 sides depending on the location and orientation of the cut.
This example shows a plane cutting an 8 noded "brick" element at some oblique angle.