Dedicated TM disks for different files?

You could do that with Time Machine, but I think it would be very inconvenient. The first problem is that you would have to change your (long?) lists of exclusions (those folders you don't want backed up) each time you switch from one disk to the other, unless you know how to create some sort of Automator action (I don't), assuming Automator actions even work with Time Machine. Second, it would back up several gigabytes of the same invisible system files on both drives, because there appears to be no easy way to exclude invisible files and folders.

Over the years, off and on, I have used a still-free (or donation-ware) app called BackupList+ (now at v8.5.2 for El Capitan). It allows for multiple backup sets, containing whatever series of folders you want in each set. It can be set to incremental backups of predesignated amounts (no more than 4 sessions' worth of incremental backups; no more than 30 sessions' worth, etc.), or you can set it to a single, non-incremental backup (synchronized folders). Its interface is slightly arcane, but you get used to it very quickly. Click the "gear-wheel" button at the bottom of the BackupList+ window to see the advanced options.

I am in no way associated with the people who produce BackupList+.

 

You can use additional tools already in OSX to do what you need a simple bash script will do the backup something like this.

Code:

#!/bin/bash

rsync -avP /Volumes/New/Disk/Storing/Files/A /Volumes/New/Disk/Storing/Backup/Files/

Add a line for each directory you want a backup for then cron job for the daily backup. You would use in Terminal as your normal user crontab -e to add a cron job similar to this.

Code:

@daily      /path/to/bash/script.sh

Which backs it up on a daily basis most likely midnight if ones I have done on linux are any indication of the default time it runs on. Now you would not likely want the vP of the -avP in the rsync line as those are not needed in an unattended script running they are for verbose output and a resume on partial copy if the sync is canceled. Also in Terminal you would want to chmod +x /path/to/bash/script.sh to make it executable so it will run from a cron job.