What's in the logfile? You're probably getting a lot of exceptions. Laravel will log the stacktrace to this file in production, rather than sending it to the browser. That's the only reason I can think that it would be filling up. There's a good chance it's alerting you to something you need to fix, especially when there's 31gb of text in it.
Check that, then look at setting up log rotation, that way you can move out laravel.log to laravel-yyyy-mm-dd.log or similar.
Inside config/app.php there is a log key, which you can set to single, daily, syslog, or errorlog. Set it to daily in order to get rotation running. Keep in mind this means you will get your logs spread across multiple days if you're not cleaning out old records.
You can use syslog to log directly to your system's logfile, which will automatically be setup to rotate out but - depending on rotation of that file - you'll lose historical tracking after a few days.