The Log Manager can rotate your logs, and can also be used to download your logs to your computer.
7.1 Using the Log Manager
Once you are logged in to siteadmin, as outlined in this tutorial, select Log Manager. To delete old logs, click the Select box to the right of the log you want to delete (you can select multiple logs), and click Remove Selected.
Log rotation can be used to automatically clear out the contents of your log files every day, week or month, or when the logs reach a certain size. You can specify how many previous logs you wish to keep. (Before the log is cleared, the current log is backed up.)