Disk-based file transfer on a Mac generally takes the form of dragging/dropping a folder from one disk to another.  There are various levels of abstraction at play here, so it will help to zero in on exactly what you want to do and how.  But in general, these dsk images you speak of would be hosted/mounted by something (i.e. Floppy Drive EMU) so as to present an icon on the desktop for dragging.

There was of course plenty of backup/restore software back in the day.  But the method I find most useful is to just plug both drives (source/target) into the same box and drag/drop away.  So, you'd plug a backup SCSI drive into the SCSI port of the SE.