Is there a native way to provide parent level group of a field in a Saved Search Group field. The csg looks like Country : State and we want out saved search to be Grouped and summed by Country only.

Have you tied grouping by a formula text that extracts the first half of the field?

Last time I did similar years ago I did a SUBSTR to extra them. For some reason now that CSG field is just giving an invalid formula error on all combinations. Maybe it will work tomorrow.

CSG as in custom segment? Maybe you can try joining to the custom record's name field