Open the Phone app
Tap Voicemail
Delete individual voicemails by swiping left on a message and tapping Delete
Tap Edit, select voicemails, then tap Delete to remove multiple messages
Clear the Deleted Messages folder if you want to permanently remove them
Contact your carrier to disable voicemail service if you want to turn voicemail off completely
Ask your carrier to remove voicemail from your line if the option is not available on iPhone