Mirroring doesn't affect the log, with the exception that the log is needed to send the data to the mirror database.

If you don't need full recovery mode, why not just script the restore of your daily backup on a second server? Or run a job after the imports that backs up your server, copies the file to a remote server and restores it? That way you would have a second copy of the data and clients could connect there in the event of an issue.

If you do need mirroring and more automatic failover, then you need to run in full recovery mode and incorporate log backups, as Gail mentioned.