Why does it mention the redemptions from Egypt and Ashur?
Radak: These were two exiles. "Ashur" refers to Galus Bavel, for Melech Ashur is Melech Bavel 1 .
Radak (23:13): Ashur founded Bavel earlier, so it is included in Ashur; those who rule over it are called kings of Ashur. However, today it is of Bavel and the Kasdim, for they conquered it.
Why does it say "v'Ashur b'Efes Ashako"?
Rashi: There was some debt to Egypt, for Yisrael lodged there and were fed there. Ashur oppressed them without any debt.
Radak: Both Egypt and Ashur oppressed them without any justification. Egypt had no right to subjugate them harshly. Initially, they came to sojourn there! Also Ashur had no reason. Yisrael did not fight them. Why did Sancheriv exiled the 10 tribes, and Nebuchadnetzar exiled Yehudah and Binyamin? Even though it was decreed [that Yisrael be enslaved], Egypt subjugated and afflicted them too much. Also Ashur - "Ani Katzafti Me'at v'Hemah Azru l'Ra'ah" (Zecharyah 1:15).
Malbim: Egypt did not exile Yisrael from their land. Just the contrary, "Ami Yarad ba'Rishonah Lagur Sham"! It was not such a great injustice to enslave them later, for Yisro entered Egypt's borders. However, Ashur exiled Yisrael from their land. It did not benefit from this; its kingdom was destroyed in the days of Chizkiyah to Efes, because they oppressed them b'Efes (without reason) and without benefit.