There are two ways to get things back the way you want them for TextEdit. The first fixes all OS X apps, and those written by Apple not included with the OS (such as Final Cut X).
Step one: Open the System Preferences and click on the General tab. By default, two options are off. Turn on the check boxes for Ask to keep changes when closing documents, and Close windows when quitting an application.
The first is particularly important to Save As since you do not want Autosave/Versions saving anything without your consent. If you don't check the first box, your original document will receive the same changes as your Save As document, defeating the entire purpose of not having your original assume all of the same changes. The second isn't necessary to Save As, but if you're like me, you also have no desire for your desktop Mac to behave like an iPad, which restores all apps back to their last state on a startup or restart whether you want it to or not.
Step two: Related to the Close windows when quitting an application check box is reopening windows when logging back in. Again, it's an iPad like behavior, which many desktop users also didn't like. Select Restart or Shut Down from the Apple menu and uncheck the box for Reopen windows when logging back in. You can then click Cancel. Your change to the check box will be saved.
Your Mac will now work like any Mac before Lion, 10.7. Apps will not launch themselves and program windows will not restore themselves on a restart or power on.
Step three: Back to Save As. Open the System Preferences and click on Keyboard. Choose Application Shortcuts in the left column. By default, the only item there is Show Help menu. You're going to add a new one. Click the + button. Where it says Menu Title, type Save As and stop. Be sure to capitalize each word. Do not put a space after "as". Three periods does not work here. You must enter a true ellipses. On a U.S. keyboard, that's Option+; (Option key plus the semi-colon).
Where it says Keyboard Shortcut, press Command+Shift+S. Click the Add button and close the System Preferences. Your screen should look like the image below.
Close any applications you may have had open and relaunch them. Save As… will now replace Duplicate in all menus where Command+Shift+S would be. Duplicate will remain in your menus, but now has no keystroke (on the desktop, Command+D will be Duplicate, as it always has been). Save As will also work as you've always used it. After saving your document with a new name, you can close the original and it will do so without asking if your want to save your changes to the original. Even better, the original closes without any of the changes applied to it. And by having the check box on for Ask to keep changes when closing documents, you can close a document that has changes without Autosave/Versions saving those changes without asking. You will instead get a choice of Revert Changes, which will have the same effect as the old Don't Save.
If you search around, you'll find Terminal commands to completely disable Autosave/Versions globally. Don't do that. If you do, then even with the above changes, Save As… will disappear from Preview. The only commands in the menu to save any file will be Save or Export. The Terminal command doesn't affect TextEdit the same way, Save As… stays in the menu. I don't have any of the iLife or iWork apps, so I don't know how it would affect those. From those reporting who have tried these steps, Save As… returns to Command+Shift+S. It doesn't matter that Autosave/Versions is active at this point. With the changes above, your Mac will essentially behave like OS X in Snow Leopard or earlier. Not that Autosave/Versions working in the background still won't slow your system down when working with large files, but at this time, you can't have it both ways.
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That takes care of Save As… globally. If you'd like to take it a step further (I do on all versions of OS X after Snow Leopard), is to replace the version of TextEdit that comes with Lion and later with the SL version.
1) Create a folder named Applications in your user account.
2) Copy TextEdit from Snow Leopard into this new folder.
3) Use Terminal to delete the version of TextEdit that comes with Lion or later from the root Applications folder. You can also open the Get Info dialogue on it and change all permissions to Read/Write. You may also need to add yourself (the admin user) as an account in TextEdit with permissions. Give yourself Read/Write access. Then you can put the newer version of TextEdit in the trash from the desktop without the OS telling you it's "required".
Since a version of TextEdit will still exist (in your user account), there's no need to change file associations. The reason for putting it in your user account is permissions. If you were to put it in the normal Applications folder, doing a Repair Permissions in Lion or later will destroy SL's versions of TextEdit, and you'll have to retrieve it from SL again. Repair Permissions doesn't do anything to user accounts, so it will remain untouched there. The SL version of TextEdit has no idea what versions or autosave is, so will behave as you're used to. That is, saving changes only when you tell it to.
