By default MySQL server doesn’t rotate slow queries log. Probably the simplest way to get rid of slow log which takes gigabytes is to use logrotate. Here’s an example:

[root@marge ~]# cat /etc/logrotate.d/mysql-slow
/var/log/mysqld-slow.log {
weekly
missingok
rotate 1
nocompress
copytruncate
notifempty
create 644 mysql mysql
}
[root@marge ~]#

If you need more than one rotated log adjust rotate values.