If you are not using CometService, you cannot completely disable logs. This is because your mySQL table is used to transport data from the sender to the receiver.
However, you can clean up the tables periodically by running the following cronjob every 3 hours:
If you are using CometService,
You can set “Save Logs” to “No” through CometChat Administration Panel.
Click on Settings tab -> Comet Service -> Select “No” option for Save logs? -> Click on “Update Settings” button.