How to delete a discussion and the response?
Short answer: you can't.
You can delete your own comments, but not your discussions, and you cannot do anything to other people's comments/responses.
You can edit your discussions, essentially making them blank, but I don't recommend this, as it'll be confusing and thus will engender further commentary, which I presume is what you're trying to avoid in the first place.
Question for a moderator: are mods able to delete threads? I know they can edit them and close them.
Yes, moderators can delete discussions.