For Linux Mint 17 based on Ubuntu you have to use this because it uses upstart as it is the way on Ubuntu 14.04 LTS:
echo manual | sudo tee /etc/init/<service_name>.override
For Linux Mint Debian Edition, it uses System V init, so you can issue:
update-rc.d -f <service_name> remove
It will remove completely the init scripts for the service. So if you are disabling it for a while and you want it in the future, better use:
update-rc.d <service_name> disable
This only change the scripts of the service from signal start to signal kill, preventing it to start.
In the future it will change to systemd for both of them.