"That's" also means "that does"

I have seen many Hollywood dialogues that use "that's" as a contraction of "that does". My assumption is that the use of such contraction is acceptable in colloquial English. Now, there has been so much fuss about using "that means' correctly, as opposed to "that's mean" that would imply totally different meaning. If "that's" is acceptable as "that does", wouldn't "that's mean" is also colloquially correct to imply "that does mean"?