For example. Lets say I wish to create something like an off axis 3x3 mod, like an axis cube. Is it possible to figure out cuts and extensions without using 3D software program to model the two cubes, extending the slices to the outer edges to determine shapes needed.
Yes of course. People were making complex shapes well before 3D printing. There's a variety of ways. Often it's a case of recognising something in the shape you can start with (like a simple extension) and go on from there. Maths may help for some parts but often you can do it by eye.