It sounds like Mint doesn't have the necessary drivers for your network hardware included by default.
Try this:
- Plug your phone into your computer with a USB cable.
- On your phone, dig into your settings and find "USB Tethering" (it's usually under 'Hotspot' or 'Network').
- Flip that on. Mint should see it as a normal wired connection and get you online.
Once you're online, go to your start menu and open up "Driver Manager". It'll scan your system and probably say "Hey, I found your WiFi card!" Just tell it to install the recommended driver, and after a quick reboot, you should be golden. Both your WiFi and Ethernet will likely pop right up.
If that doesn't do the trick for some reason, we can dig a little deeper. Just open up the Terminal, run this command, and paste the output here for us:
inxi -N