A "Mitanni language" did not exist. Rather, Mitanni was a multiethnic and multilingual state, with people predominantly speaking Akkadian – the lingua franca of the ancient Near East – and Hurrian. Akkadian was quite well attested throughout Near Eastern history and survived until the end of the 1st millennium BCE. Hurrian died out at the end of the Late Bronze Age, but its relative Urartian survived into the Iron Age.

The elite in Mitanni seem to have spoken Hurrian. Hittite and Assyrian texts refer to the king of Mitanni as the "king of Ḫurri-land" (LUGAL KUR ^URU Ḫurri) and the "king of the Hurrian troops" (LUGAL ERÍN.MEŠ Ḫurri), and the letter from Tušratta found in Egypt was written in Hurrian.

While a small segment of the Mitannian population may have originated as an Indo-Iranian speaking group – or at least been in close contact with such a group at one point – the exceedingly few examples of Indo-Aryan words in Mitannian texts are fossilized, and there is virtually nothing to suggest that the ruling class of Mitanni (or anyone else in the kingdom, for that matter) spoke anything other than Hurrian and Akkadian by the Late Bronze Age. This is very different from, say, the Luwian interference in Hittite texts or the West Semitic interference in the peripheral Akkadian of the Amarna letters that reveals the bulk of the population was speaking a language other than the official languages used for administration. As Eva von Dassow put it in "Levantine Polities under Mittanian Hegemony" in Constituent, Confederate, and Conquered Space: The Emergence of the Mittani State,

A tiny quantity of Indo-Aryan vocabulary and proper nouns became incorporated into the Hurrian language of Mittani, while also spreading among realms with which Mittani interacted, over the course of the empire’s floruit. Apparently no one in Mittani spoke the Indo-Aryan source language, for the borrowed lexical items were unproductive in the borrowing language, there is no Indo-Aryan grammatical interference therein, and no other extant evidence indicates that the donor language had ever been the living cultural property of any part of the kingdom’s population. The scant Indo-Aryan linguistic material does not attest the presence, much less the dominance, of an Indo-Aryan-speaking population.

The overwhelming majority of texts from Mitannian sites (Tell Brak, Alalakh, Tell Bazi, Nuzi, etc.) are in Akkadian rather than Hurrian. Most of the extant Hurrian texts have been found at Hittite sites in Anatolia, particularly Boğazköy/Ḫattuša and Ortaköy/Šapinuwa. The presence of Hurrian religious texts in the Hittite empire is due primarily to the influence of the Hurrianized region of Kizzuwatna/Cilicia in southern Anatolia and the importance of queens from the region such as Puduḫepa. (For more on this, see Dennis Campbell's article "The introduction of Hurrian religion into the Hittite empire.")

Hey there,

Just to let you know, your question is fine, and we're letting it stand. However, you should be aware that questions framed as 'Why didn't X do Y' relatively often don't get an answer that meets our standards (in our experience as moderators). There are a few reasons for this. Firstly, it often can be difficult to prove the counterfactual: historians know much more about what happened than what might have happened. Secondly, 'why didn't X do Y' questions are sometimes phrased in an ahistorical way. It's worth remembering that people in the past couldn't see into the future, and they generally didn't have all the information we now have about their situations; things that look obvious now didn't necessarily look that way at the time.

If you end up not getting a response after a day or two, consider asking a new question focusing instead on why what happened did happen (rather than why what didn't happen didn't happen) - this kind of question is more likely to get a response in our experience. Hope this helps!