Maybe: "Mine is" when dealing with singular things because dealing with more than one you wouldn't respond "mine is" would you? if you were dealing with more than one the response would be "mine are". I guess "mine's" a better alternative rather than shorten another word for "mine are".

I think the reason is partially due to laziness but I can understand how that word can come about. For example: (In conversation). John: I have a red 1990 Honda Civic. Dave: Really? I have one too, but mine's grey.
I guess you can say "mine's" short for "mine is". It's as confusing as Jimmy is supposedly short for James. Maybe if it was just Jim.