My server's MySQL slow query log is growing day by day (37 MB now) so I want to rotate it. If I move current log file to another folder then will MySQL automatically create another log file? Think of it like I am deleting current log file, so will MySQL automatically create a new one when another slow query comes?
You can use
logrotate script to periodically rotate MySQL logs, and possibly keep a limited number of previous logs (to save space). You can configure it with any schedule you like.
Personally, I found it easy to configure using Webmin GUI