Normally in the middle of the Kaddish (of the various varieties, see prior column at this link), we say the line (in Aramaic):
יִתְבָּרַךְ וְישְׁתַּבַּח וְיִתְפָּאַר וְיִתְרוֹמַם וְיִתְנַשֵּׂא וְיִתְהַדַּר וְיִתְעַלֶּה וְיִתְהַלַּל שְׁמֵהּ דְּקֻדְשָׁא, בְּרִיךְ הוּא, לְעֵֽלָּא מִין כׇּל־בִּרְכָתָא וְשִׁירָתָא תֻּשְׁבְּחָתָא וְנֶחָמָתָא דָּאֲמִירָן בְּעָלְמָא, וְאִמְרוּ אָמֵן
May the name of the Holy One be acknowledged and celebrated, lauded and worshipped, exalted and honored, extolled and acclaimed—though God, who is blessed (berikh Hu), is above all acknowledgment and praise, or any expressions of gratitude or consolation ever spoken in the world. And we say amen.
During the ten days of teshuvah, which are bracketed by Rosh Hashanah and Yom Kippur, we add a bit of extra elevation to God’s status, and we say in place of those larger blue words above:
...לְעֵֽלָּא לְעֵֽלָּא מִכׇּל־בִּרְכָתָא וְשִׁירָתָא...
...is truly far beyond all acknowledgment and praise...
Literally, we say “higher, higher.” (Some versions add the conjunctive vav: le’ella ul’ella or “higher and higher,” לְעֵֽלָּא וּלְעֵֽלָּא.)
Now as to why the grammar changes in the word following, the prefix “mi-” means “from” and is the shortened form of the word “min,” which also means “from.”
In the evolution of the language, the letter nun has historically been absorbed into other letters. So over time, “min” became a prefix to the word in front of it, without the nun. In Hebrew many prepositions appear as prefixes.
(As an aside, your correspondent recommends reading Grimm’s Law, which was written by one of the Brothers Grimm and covers how languages generally evolve. Gripping reading.)
Thus, the phrase at hand means the same thing whether using the prefix “mi-” or the word “min.” However, there is a Kabbalistic tradition that one should not change the number of words in a prayer. Thus it is likely that the scholars felt that adding the extra word required adjustment to delete another word, which was easily accomplished without changing the meaning.
As we reach higher for ourselves during the High Holidays, we utz God a little higher, as well, raising the bar.