Yeah... this is a common issue... so I should start by explaining that when you create segments (whether they are permanent public segments that are available in your components area, or they are AdHoc segments "tied to the specific report"), there is actually a segment with a proper ID create in the DB (you just don't see it).
So let's say you create a report called "Report A" and in Report A, you created a segment called "Page X".
Even though you haven't saved the segment publicly, in the background it's been created with a ID 12345.
When you make a copy of "Report A" and call it "Report B"... it's still linked to the segment with id 12345.
So any changes you make the this saved segment will affect both reports.. as you are saving changes to ID 12345.
Best rule of thumb is, if you need to change a segment for the new report, create a new segment, but of course, if the segment is just in the report... there' no way to create a copy of it to make changes on... If the segments is a "public" segment in your components list, you can duplicate those...
In some ways this is a nice feature.. if you need an adhoc segment used in multiple panels, or added as breakdowns or stacked with metrics in multiple places in your report.. it means you only need to update the segment once and all the places will get the changes (rather than having to make the change multiple times)... but it does mean that when it's copied to a new report, the segment is still shared and changes will affect everywhere.
It would be nice if AdHoc segments had a "Save As Copy" feature to make this easier than having to rebuild the segment completely for a slightly different change...