For any calibre there is, someone has killed a deer with it, or claimed too.

I'm sure someone out there has "killed a deer" with a BB gun.

I've even heard a story about a deer "wandering" onto a military target range, just as .50 cal. practice was commencing... no deer left when it was over.

The .17 HMR deer kill... it's either a tall tail, or an extremely well placed head shot at close range, and it's still poor judgement.