"MIN" doesn't mean anything. All this means is that the three letters "MIN" were written in error at some point in the original document and then deleted or crossed out, and are not valid. If you prefer, you can say "The deleted letters "MIN" are not valid", as suggested in this previous question:
http://www.proz.com/kudoz/spanish_to_english/law_general/922...
Compare also: http://www.proz.com/kudoz/spanish_to_english/law_general/916...

So then to your question: why does "MIN" not appear in the document you have? Simply because what you have is a certified copy of an original birth entry. This original, probably handwritten, contained a correction; the letters "MIN" were written in it at some point and then deleted. By law, this fact had to be certified at the end, before the signatures, with the formula "testado - min - no vale".

When the copy of the birth entry was made, this formula certifying the correction in the original was copied as well, but only the corrected text was copied, not the actual deletion. So since the letters "MIN" were not valid, they were not copied. This is standard practice.

Here is a page containing a copy of a Mexican birth certificate. Note that the text contains no corrections, but at the end it says "Testado que. = No vale". The word "que" was deleted in the original, but since it was not valid it was not copied. However, the formula certifying its deletion was copied. This is just like your example.
http://repetto-yucatan.blogspot.com.es/2012/03/transcripcion...

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Note added at 1 hr (2013-04-22 17:29:47 GMT)
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The same issue arose in this previous question. Here is what I wrote about that case:

"One more point here. You may very well find that the text in front of you contains no corrections or alterations. So it is in the Salvadorean example I cited above. The point is that someone has made a typewritten or printed copy of a (probably) handwritten entry in the register of births. This original entry contains corrections, and these are certified at the end as I've explained, and then someone has copied the correct text and the certification but not the actual textual corrections. If your document is like this (as I expect it is), you probably can't identify what this correction refers to, because you have only the corrected text."
http://www.proz.com/kudoz/spanish_to_english/law_general/507...