OK; embedded in the last three comments are several questions. I'll try to answer them all.
I have a total of 4 HDs.
1) My internal HD is 320 GB with 212 GB free. The in use portion of the drive, in addition to the apple stuff that came on it contains primarily my programs, mainly two releases of Photoshop plus Bridge, Lightroom and TeX Shop. Also Firefox and all my emails.
2) I keep all of my data, primarily photographs on a 3 TB external HD with 1.36 TB free. I back this external HD up to a second external HD daily. That other HD is also a 3 TB drive with 1TB free. I have, for the life of my computer used this 2 HD setup for my photography. dougstocks.com if you are interested.
3) Finally, my newest HD, is the My Passport which I set up fairly recently to use with Time Machine to keep a BU of my internal HD. It is (I think) a 1TB drive. When I first encountered this problem, I thought that the My Passport had failed, so I bought this newest one. I started backing-up my internal HD probably only about 2 years ago. I think I read that it was a good idea. Further, prior to that time, if one of my programs failed I could always buy a new one. But when Adobe stopped selling their major programs and initiated their subscription scheme instead, I figured that I ought to have a BU of PS & Bridge. So, the small My Passport is used just to have an extra copy of my programs.
4) You are, of course, correct. Second Copy is a Windows program. I should have looked instead of relying on my notoriously faulty memory. What I am actually using is Carbon Copy Cloner.
5) As implied by above, I primarily use my machine for the post-processing of digitally captured photographs. Secondary uses are emails, search for stuff using Firefox or Safari., Occasional use of TexShop. Tracking Investments using some on-line Quicken Program. Accessing bank and investment accounts. with occasional stock trading. I also use my machine to access and maintain a few photographic web-sites. Oh yes, I also infrequently use Open Office for various minor things. Annually, I use TurboTax. I recently bought MacBooster 2 and use it frequently. It has really speeded up my machine.
6) I will not swear to this, but my recollection is that the Mac Mini has four, maybe five USB ports. All are in use and I think each one has a hub on it. So, there are several things connected to the computer via USB. I have had no problems with anything except those two "My Passport" HD. There is one other device, a printer I believe, connected to the same hub as the My Passport. It works fine. No, I have not tried disconnecting the other stuff. My personal preference would be to just call it quits on the My Passports - but I do worry about someday needing another copy of Photoshop For example, I might buy a newer mini with 16 GB RAM. That sure would speed up PS.
7) My present Mini is, I think, late 2008. I tried disconnecting the My Passport, but before my Mac could see it again, I had to do an SMC reset. But even then, it vanished again in less than 5 minutes. The My Passport could be faulty, but, if so this would make two in a row that were faulty.
8) Your copying your files back onto your restored HD is what I envisioned doing, if the need ever came up. However, knowing Adobe, they may have some built in feature that prevents such a thing.
If you have any suggestions, I will gladly consider them, but as indicated earlier, I'm about ready to just scrap the idea of keeping my internal HD backed-up.
Many thanks for you kind assistance.
Doug