How would I correctly punctuate the following:
Did you ever say, "Isn't that a cute puppy."
It's a question, evidenced by "Did you", but "isn't that a cute puppy" is not a question even though it is at the end of a question.
You have two question here:
There all have interrogative words: "Did", "Isn't".
There is a difference with affirmative questions like "So you’re Harry’s cousin?". Without the question mark, it is an affirmation, not a question.
Strictly speaking, this two questions require a question mark. So you should add two question marks. But the usage is to omit the one in the citation:
Did you ever say: "Isn't that a cute puppy"?