After continuous running of Mysql server, I've noticed that /var/lib/mysql directory uses too much disk space. The reason of that problem was a set of mysqld-bin.xxxxxx files. Each of that file was 1GB in size. First I thought that I can stop the Mysql server and remove that files, but I didn't want to act this way because there was sensitive data in databases that I didn't want to loose. So I found the better way to achieve this. Connect to Mysql server and perform the following
mysql> flush logs;
mysql> reset master;
That's it! After that the all logbin files should be removed. Also you can disable mysqld-bin logging completely by commenting out log-bin line in my.cnf and restarting Mysql server daemon.