Luckily, it's easy to save a voicemail from your iPhone, Android or old non-smart phone. Let’s start with iPhones.
Most phones don’t make that as easy as it ought to be. Apple’s iPhone will back up voicemails to your computer along with everything else, but they’re stored in a funky file format that’s not easily played by most software. Most Android phones, meanwhile, store your voicemails on off-site servers.

The effing spammers are using this frequently. I wish Sprint would turn this off. Their G.D. spam goes directly to my mailbox without me being able to kill the call first.
With this method, you don’t need a third-party app. Call the person you want to chat with, then tap the “Add Call” button on your phone’s screen. Dial your own phone number—the one you’re calling from. This will take you to your voicemail. Once your voicemail has started recording, tap the “Merge Calls” button on your screen. Now, you’ll record your phone conversation onto a voicemail message. When you’re done with the call, you can tap the share button to export it to your Mac via Airdrop, to the Voice Memos app, or transfer it via email or text message. The file is recorded as an M4A, so depending on what you want to do with it, you may need to convert it to MP3 before uploading it to other apps.