Is "mine's" a valid contraction?

Yes, but...

On the one extreme, just about any contraction is valid.

On the other extreme, there is a certain set of extremely common contractions (the negatives of auxiliaries in particular) that everyone agrees are good English, and after that you will find some people objecting, if only as a matter of taste.

The contraction of ’s for is is probably the next safest. Combining it with a genitive makes you slightly more likely to have someone object (because they argue it could be confused with genitive ’s) though that would still be more a matter of taste than correctness.

As such, I'd have absolutely no qualms about using it in informal English, but I might consider expanding the contraction in formal English; not so much to be correct, as to be inarguably correct.