richprice79,
Just try
Disk Warrior. You'll have to get the latest version, as the earlier versions won't work on Snowy, but Disk Warrior saved my bacon before. I think it's worth every cent of the $100 selling price.
I also had a Seagate, but I bought mine from Costco. It was a 1.5TB that was only $10 more than the 1TB WD right beside it. Mine only lasted a few days over two weeks and I began to notice that it had problems finding things like .. . oh ... my iTunes library

After two days of this, Disk Utility recognized that a drive existed, but was unable to do anything else with it. A friend of mine lent me his Disk Warrior disc to attempt a data recovery and I estimate that I was able to restore approximately 98% of the lost data onto a second external HDD.
Of course, after that, the POS Seagate drive was wiped and promptly returned to Costco, who has an outstanding return policty, btw, after which the aforementioned WD HDD was purchased (no issues to this day with that one). I will never again use Seagate drives, for any reason.
To make a long story short, you will need another HDD with at least the same capacity of the Seagate drive, and a copy of the latest version of Disk Warrior. Depending on when you purchased your Mac Mini, you may be able to boot off the Disk Warrior disc, or you can put the Seagate drive in an external enclosure. Using the Disk Warrior disc, you will most likely be able to restore most, if not all of your lost data. Of course, YMMV, depending on the condition of the Seagate disc.
HawaiiMacAddict