The only reason you will be turning on circular logging is if you've not planned your servers correctly, i.e. you've run out of disk space. If you're doing it for any other reason then have a good look at what happens when you turn it on.
If you're thinking of moving the log files then firstly make sure your backup is deleting the log files regularly. If it is, and you're still running out of space, then I would strongly recommend installing a new drive and moving the log file location rather than turning on circular, as if you turn off the logging you have the potential to permanently lose emails that are not yet backed up, which in many environments is just not an option. Obviously ensuring the new log file drive is large enough and can be backed up is common sense. It might however be a good time to get in a new server as, if you're out of space, you're probably running an old server and server version.

You'd probably realise that these log files contain transaction data that is constantly being committed to the database. If you move them you would have to at least pause transaction to the database which is effectively downtime anyway so I'm quite sure that's why you must dismount your store first. But I guess if you knew what you were talking about you wouldn't have posted in the first place.

When will Microsoft get it that it is unacceptable to take a server offline to change a configuration option? I guess MS software is just for companies that don't need 24/7 uptime. I've got to take servers offline to install windows updates and to change the circular logging options.