That is a huge scratch/gouge. This is the issue here.. Don't ask me how it was done. All I know is that it didn't occur during the minting of the Dime.
I would think jammed in one of those coin. Sorters that spins everything around horizontally like a washing machine tornado to sort it, Just a guess. I've come across a couple of the old sorter machines at credit unions that jam up badly with dimes like every minute until the jam can't be cleared and they need to shut it down for the repairman to come. I've seen him working on it pulling out bent dimes with pliers from the spinning mechanism.
It's possible because whatever instrument/material was dragged across the obverse side of this coin, when it came in contact with the coin's raised edge, it then traveled along the raised edge. If this instrument/material had more thrust, it would have went over the raised edge and not along it. Like a car skidding across a freeway and into a sound wall. If the car had more thrust, it would have traveled over and not along. Think of it as, following the path of least resistance.
Looks like the edge of a screwdriver started digging on one side, hit the rim and skipped off to the right.
One question amigo-'is a damaged coin a damaged coin if it's damaged by the mint after minting process?
Normally most damage incurred after striking is considered PMD. Here’s a good reference. http://www.error-ref.com/?s=Post+mint+damage+