Deck List Creator is designed to easily save copies. 

Click the Copy button to duplicate an older list. If you are duplicating a Standard list, you can copy it to a Standard list [Copy S] or an Expanded list [Copy E]. Expanded lists can only be copied to an Expanded list [Copy E].

Once you save it, it will be its own deck list. Remember to give it a name! 

You can delete the older list if you want, by clicking the Delete button on it. (Don't worry, it will ask you for confirmation.)