Unfortunately, no - there is no process. or failure of a process, that can occur in the striking of a coin that can result in both a clad coin coming out looking coppery, and a clad coin coming out with a giant gash on it. One or the other might theoretically happen, but not both at the same time. The damage has therefore not happened in the mint.
What might have caused such damage? It's difficult to tell for sure, as lots of things can happen to coins once they're out there in the hands of bored, creative, careless and curious people. A good place to start might be superglue. If a dime is superglued onto an outdoor surface, then torn off of the superglue some time later, it might end up looking something like this. The brown stain is caused by the superglue, and the tear caused by the violence of the coin being separated from the surface.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis