ironuckles
You'll first need to create a free Google Voice number by going to voice.google.com or by installing the Google Voice app and going through the instructions to create a number. It's free for US domestic calls/texts, but they require payment for international. For the purposes of just using it for voicemail (which is essentially just a received call), it's free. You may want to redo the voicemail greeting to your liking.
For conditional call forwarding so that voicemails go to google voice instead of mint mobile:
Google Voice instructions:
https://support.google.com/voice/answer/165656?hl=en
For Mint mobile specific instructions:
https://www.mintmobile.com/help/how-to-turn-on-off-call-forwarding/
You'll want to do the call forward instructions for each of the 3 conditions, not for all calls, otherwise all call will forward to google voice instead of just the missed/rejected calls.
To actually see the voicemails, you'll need the Google Voice app (requires play services) or create a progressive web app with your browser (like Vanadium). Google Voice will provide push notifications whereas the PWA will not.
Note that this a semi-permanent thing that is tied to your service with mint mobile, not to your device. So even if you switch devices and keep the same sim, it will still forward to google voice. You'll need to enter the commands to revert the call forwarding back to normal, which you should be able to find via googling or by contacting mint mobile support. It probably will use T-Mobile commands since Mint Mobile uses the T-Mobile network.