How to determine why a MySQL server has become slow and requests sometimes time out?
You need to tune your database. This is a complicated process with many variables and decision trees. Without specifics we can only really get you started here.
If you have a script that runs lots of SQL and slows down your DB, and your cpu and memory usage are fine while it's running, then you are probably running into I/O problems. i.e. You are hammering the disk. You need to look through the SQL used in the script and tune it. For example, it might be generating lots of full table scans or creating too many transaction logs that are slowing down the DB. To start with, check if any unneccessary full table scans are taking place, and see if you can add indexes to the relevant columns to reduce the I/O. then report back and we can go from there.
The above linked MySQLtuner script is excellent but understanding the results may be challenging for you if you are inexperienced with databases. Do read the disclaimers on the main page before you get started: https://github.com/major/MySQLTuner-perl