Open the Phone app
Tap Voicemail
Select the voicemail you want to save
Tap the Share icon
Choose Save to Files, AirDrop, Messages, Mail, or another app
If needed, tap the voicemail and use the share option from the details screen
To keep a backup, save the voicemail to iCloud Drive or another cloud storage app
To save it as an audio file, export it through the Share menu
To record it externally, use another device or app to capture the audio while it plays