I just tried to uninstall MySQL on Debian via

apt-get remove --purge mysql-server

apt-get remove --purge mysql-client

apt-get autoremove

and wondered that the directories /var/lib/mysql /etc/mysql still existed after the commands. Then I recognized, that a

apt-get remove --purge 'mysql-server.*'

is doing better and removes everything.

Note:

if you get a

/etc/init.d/mysql: WARNING: /etc/mysql/my.cnf cannot be read.

error when you try to re-install MySQL, try a

apt-get purge mysql-common

and try to re-install again.