How do I disable MySQL on Linux from starting on boot or statup?

MariaDB use systemd as does MySQL. To disable MySQL or MariaDB, from starting on bootup, run

systemctl list-unit-files '*mariadb*' '*mysql*'

If you see mysql.service, try disabling that one first.

sudo systemctl disable mysql

Now you can start and stop MySQL with

sudo systemctl stop mysql.service
sudo systemctl start mysql.service

In Ubuntu 18.04, sudo systemctl disable mysql will prevent mysql-server from autostarting on boot.

For linux, there are 3 main init systems: Systemd, Upstart and SysV. Although nearly all Linux systems run on Systemd. The other two init systems might also co-exist in your system.

For Systemd, use command sudo systemctl disable mysql;
For Upstart, use echo manual >> /etc/init/mysql.override;
For SysV, run the following command sudo update-rc.d mysql disable

If you'd like to find which init system is running on your server, please read this answer.