Set Start Point on Geometry cut with "Cut Shapes"

There are multiple things going on if I’ve understood your explanation correctly:

  1. Set shape start point will only work on a simple object. So no grouped objects. Ungroup to be able to do this.
  2. However, I think in this case you may not have a truly closed shape. Grouping won’t get you a closed shape. You’ll need to join the segments. See here for more info on this:
    Having trouble with closing shapes - #5 by berainlb
  3. A shortcut for what you’re trying to do: instead of using cut-shape, use another closed shape (e.g. rectangle) as a “cutting” tool, position it, select base object, add “cutting” shape to the selection, Tools->Boolean difference. This will automatically result in a simple closed shape.