If you can tolerate the bottom deviating from the original curve by some small amount (like 0.02 units) then you could do the cut like this instead and the bottom part should be smoother.
Getting the top to be smoother is probably going to be harder, the base surfaces have different surface normals at the point that they touch.
Thx but it's not on line! ;)
There is another one inside Free DesignSpark Mechanical! ;) (A SpaceClaim light)
but it's some tricky! ;) and also not online! :( https://www.rs-online.com/designspark/mechanical-download-and-installation
Import your Step Moi File - draw anything a sphere for example
Call the Arborescence - Lock the Sphere - You can manipulate and edit your moi File! ;)
Here i keep the sphere but can erase it and change the color of the cube! ;)
It's also here a PDF3D exported and created inside Design Spark Mechanical! ;)