Sorry, I think I misunderstood your original question.
When you quit with a document open, the system saves state restoration information, including the URL of the document file, plus UI state such as window position and possibly custom information you provide. I thought you were asking about getting rid of this UI state, which is unnecessarily tricky to do.
What I think you actually want is to not re-open the previous document at all. That's not especially difficult, and you can approach it different ways:
— You can use the scheme option during development, and leave it on. The state information is ignored, so your document should not re-open. (But you'll have to do something when you eventually turn the option off, because really old state information will be there.)
— If your app crashes or stops at an exception, you can use the debugger to find the URL of the old document, and delete it manually via the Finder.
— If your document hasn't been saved yet, the normal place for the untitled document file is ~/Library/AutoSave Information. You can look in there for a file or folder with a name like "Unsaved XXX Document", where "XXX" is your app, and move it to the trash.
My advice still stands, though. Regardless of what stage of development you're at, your document opening code should handle an invalid file reasonably gracefully, and early in development there's nothing terrible about a couple of lines of temporary code that deals with the situation. It's up to you if you don't want to do this, but you're gonna have to write code that anyway, sometime.