I live in Alabama. I took my 1 year old male Yorkshire Terrier to
PetCo for a typical Pet Cut. When I picked up my dog, his hair was
less than half an inch long. He looks HORRIBLE. He's received this
same cut from them before therefore I KNOW that they know what it's
supposed to look like. All they offered me was a refund and free
sweaters. Can I sue? If so, on what grounds and for how much?

You can sue anybody you like anytime for as much as you like. But it's
not a good idea. The only sure winners are the lawyers. Better forget
it! The dog's hair will soon grow again.

You want to SUE??? Look -- get Fido the free sweater to keep him warm
for the time being, and go somewhere else for pet grooming. It's
hair/fur -- it'll grow. It's not like they lopped off the poor dog's
ear!

Go ahead and sue.  Even judges appreciate a good chuckle every now and then.

It's not as bad as you think.  Fido isn't as upset as you are, or as
you would be if a hairdresser had done the same to you.  Your best
compensation will be bad mouthing the place to all your friends.