How can I delete all voicemails from my iPhone? I would like to bulk delete all the voice mails from my iPhone but it appears I need to first delete each one (multiple taps on each message) and then bulk delete them all from the "deleted items" sub folder.

Is there a way to more efficiently delete all voicemail?

n.b. I have an iPhone 5 with iOS 7 on Verizon that isn't jailbroken but would welcome any answers that work for whatever OS / carrier even if a jailbreak is needed
Via swipe left on multiple voicemails you can delete them, and on the Phone app, you can even "delete all" of them.

But to delete Permanently all voicemails Permanently, meaning could not be recovery by any software, you should try iMyfone Umate.