Does galvanized metal rust where the zinc is gone?
I don’t want to give you “The Slip” so I’m doing this “With Teeth” in, but even Kurt Cobain and the Foo Fighters knows that when you strike a galvanized coated nail with a hammer, some galvanizing comes off and the head of the nail will rust quicker than the rest of the nail. So, yes, it will rust when cut off.