For several reasons.

First, assuming by "Semitic sources of history" you mean the Torah, the Old Testament was written well after the life of Abraham, and perhaps even after the kingdom of Mitanni ceased to be a power. Therefore the actual writers of the Old Testament would have had little to no knowledge of the Mitanni.

Second, the kingdom of Mitanni was not part of Abraham's sphere of influence. They had nothing to do with the development of the people of Israel. The same can be said for a large number of ancient peoples, such as the Luwians, the Eblaites, the people of Mari, the Hatti (not the same as the Hittites, spoke a different language), etc. Just because they existed perhaps around the same time as Abraham, does not mean that Abraham had anything to do with them. The Biblical writers would not have cared about the existence of the Mitanni, because they had no impact on the story of Abraham.

Third, we do not have any direct evidence of Abraham's existence. This is not the same as saying he did not exist, merely that we have no way of finding out. There was very little writing at that time, especially outside of Mespoptamia and Egypt, and it would be impossible to find evidence of a named person unless they had something written about them. Abraham spent most of his life as a nomad, and therefore would never have had anything written about him by any of the people that could write.

In short, the Mitanni are not mentioned in the Old Testament because they weren't around when the Bible was actually written down, and because Abraham never interacted with them. The Bible is not a history textbook. Yes, it can tell us things that we can relate to history and learn some things about history, but that is not its purpose. There is no reason for the Bible to mention the Mitanni.

If you have any more questions about this, or if I have been unclear, please let me know and I will attempt to address them.