Your description sounds like you think the "Save As" is working more like a "Move", but I can assure you that the "Save As" should allow you to take any existing report and save a copy of it with another name and/or in a different location.
I have just tested this to confirm as well and was definitely able to do what you describe so you can re-use the same layout and objects and just change the filters.
Is it possible that you saved the report to a different location (i.e. different folder, or Private versus Public etc)? You might want to use the "Search" box to make sure you can list all occurrences of the report matching a keyword in the name - it might be that it is hiding in a folder you didn't expect.
I was looking for this topic about Reports and then I found here in your post. Please, could you to give me a add information about the Filters? Aren't they transfered to new report after the "SAVE AS"? Is there a other way to do this? (to Create a new Report from a existent report with all layouts, objects and filters ).
