I assume that you don't need MySQL anymore and you have already taken backup of your important databases. I suggest you to take backup of your important MySQL databases.

Note: Your all mysql data will be lost.

First make sure that MySQL service is stopped.

sudo systemctl stop mysql

Remove MySQL related all packages completely.

sudo apt-get purge mysql-server mysql-client mysql-common mysql-server-core-* mysql-client-core-*

Remove MySQL configuration and data. If you have changed database location in your MySQL configuration, you need to replace /var/lib/mysql according to it.

sudo rm -rf /etc/mysql /var/lib/mysql

(Optional) Remove unnecessary packages.

sudo apt autoremove

(Optional) Remove apt cache.

sudo apt autoclean

all the above solutions are correct but I would try with

sudo apt-get remove --purge mysql*
sudo apt-get autoremove
sudo apt-get autoclean

This will uninstall all mysql related packages.

This will remove mysql 5.6 from ubuntu 15.04

sudo apt-get remove --purge mysql-server mysql-client mysql-common
sudo apt-get autoremove
sudo apt-get autoclean
sudo rm -rf /var/lib/mysql
sudo rm -rf /etc/mysql

First you need to stop your mysql server from service.

sudo service mysql stop

Then You can use purge command to uninstall

sudo apt-get purge mysql-server mysql-client

Note: the above based on your package list. I have installed both server and client. This will for your convineient

I don't use Ubuntu much but what I think you should try is what I did.

I first typed this in command line : sudo apt-get remove --purge mysql-server mysql-client mysql-common,

then followed with this below : sudo apt-get autoremove

and finally typed this : sudo apt-get autoclean.

I found that it was removed.

Completly uninstall mysql:

sudo -i
service mysql stop
killall -KILL mysql mysqld_safe mysqld
apt-get --yes purge mysql*
apt-get --yes autoremove --purge
apt-get autoclean
deluser --remove-home mysql
delgroup mysql
rm -rf /etc/apparmor.d/abstractions/mysql /etc/apparmor.d/cache/usr.sbin.mysqld /etc/mysql /var/lib/mysql /var/log/mysql* /var/log/upstart/mysql.log* /var/run/mysqld ~/.mysql_history
updatedb

Based on this answer and many others...

I forgot the MySQL root password and needed to reset. I tried this, but it didn't work, because it kept saying "can't write logs" or something similar.

My solution was to completely remove MySQL from Ubuntu 13.10 and fresh installation.

sudo apt-get remove --purge mysql-server mysql-client mysql-common
sudo apt-get autoremove
sudo rm -rf /var/lib/mysql

I had to run the last command because Ubuntu sometimes keeps some libs even you try to purge them all.

Now, I use this command to install MySQL server and client:

sudo apt-get install mysql-client mysql-server

When I tried sudo apt-get purge mysql* it didn't work.

Purged mysql5 with:

sudo apt-get purge mysql-*

Then for cleaning up:

sudo apt-get autoremove
sudo apt-get autoclean

Try this, It will fully wipeout out every single file of MySQL from your system:

sudo service mysql stop  #or mysqld
sudo killall -9 mysql
sudo killall -9 mysqld
sudo apt-get remove --purge mysql-server mysql-client mysql-common
sudo apt-get autoremove
sudo apt-get autoclean
sudo deluser -f mysql
sudo rm -rf /var/lib/mysql
sudo apt-get purge mysql-server-core-5.7
sudo apt-get purge mysql-client-core-5.7
sudo rm -rf /var/log/mysql
sudo rm -rf /etc/mysql