This overlaps with a question @Cam asked in a different thread and to which I responded. Closed open polysurface which openings dont have closed, planar loops of edges
@Cam Do you have experience with any other design software or similar?
Rhino works with surfaces, not volumes. Trim or Split a surface and the result will have naked edges. You can then close the surface if desired, either by creating a new surface or using all or part of the surface used to Split or Trim.
Usually the easiest way to model symmetric objects is to model half the object and then mirror it.