I have two computers here running Linux Mint (Mate). Both were version 18.3, which Mint stopped supporting at the end of April.
Upgrading Linux Mint isn't as straightforward as upgrading Ubuntu. Until I gave the attached upgrade instructions a shot, I would usually just back up all of my data, and install a fresh copy of Mint.
Pay particular attention to the display manager section on page 2. You must install LightDM and remove MDM if indicated.
On both machines, I backed up my Home folder (including hidden & config files) manually into a tar.gz file. I used Timeshift to create a backup of the system files to an external (ESATA) 500 GB HDD partition formatted to Ext4.
The upgrade ran flawlessly on both machines. My slower machine (Intel Duo-Core + 12 GB RAM) required a little over 2-1/2 hours to complete. The faster machine (AMD FX-8120 8 Core CPU / ASUS Sabertooth 990FX MB, 24 GB RAM) completed the task in just under 2 hours.
You'll be using the 'mintupgrade' tool to do the actual work. It has a "dry run" mode you should use to pick up any conflicts or issues. Once you get a clean "dry run", it's all very easy to complete the upgrade.
Linux Mate 18.3 was very popular, and I'm hoping the attached upgrade instructions will help get any 18.3 users up to 19.3 without a complete re-install.
The URL to the upgrade web page is: https://community.linuxmint.com/tutorial/view/2416