I couldn't find any way to edit a theme from my Themes and save it as a new theme. It can only save over the old one. This is a handy feature on the iOS app; when you touch the checkmark, it asks you whether you'd like to "save a copy" or just "save changes".
I found this feature very useful on the iOS app to try out different variations of a theme I made & like a lot, without butchering the original one that worked well.
So far the only way that I've been able to do anything like this is just by clicking "edit" on a theme that someone else created. I'd like to do the same thing on a theme I've created without altering the original.