Saving and managing attachments in the stock iPhone email app?
Dropbox's email management service app, Mailbox, allows you to open attachments in Dropbox or iFile, which in turn saves the attachment to your /var/mobile/Documents folder, but then again, this same thing happens in the stock Mail app (minus the Dropbox integration). What happens is iFile just registers itself as being able to open any file type, so that any application can open its files in iFile. This is how almost every application does it - they simply let iFile do all of the filesystem handling, so they don't have to (it's tricky on iOS; just ask the guy who made Sandcastle).

If that doesn't fit your needs, however, there is a paid jailbreak tweak called Attachments+ for Mail that should do everything you're looking for, and it integrates directly with the stock Mail app (plus, it even looks like it uses Sandcastle), and it's recently been updated for iOS 7.