Doing this on CentOS 7 64 bit and MySQL 5.6 community edition

Sometimes it is better to put mysql in a separate partition than its regular location

Typically the mysql database are located in /var/lib/mysql

I want to change it to /var/data/mysql 

Modify the paths as required in the below commands

stop mysql

systemctl stop mysqld.service

create new mysql data directory

mkdir /var/data/mysql

modify /etc/my.cnf and point to new data directory – add the client section to the top

[client]
port=3306
socket=/var/data/mysql/mysql.sock

[mysqld]
datadir=/var/data/mysql
socket=/var/data/mysql/mysql.sock

copy all files from /var/lib/mysql to the new directory /var/data/mysql

cp -r /var/lib/mysql/* /var/data/mysql

permissions for the new directory

chown -R mysql /var/data/mysql;
chgrp -R mysql /var/data/mysql;
chmod -R g+rw /var/data/mysql;

also modify SELINUX settings to allow mysql to use the different path

# add context and make it permanent 
semanage fcontext -a -s system_u -t mysqld_db_t "/var/data/mysql(/.*)?"
restorecon -Rv /var/data/mysql

start mysql

systemctl start mysqld.service

MySQL should start cleanly.
You can verify the change by creating a test database.
Then go to /var/data/mysql and you should be able to see the new database there