Does anyone in Tanach ever get divorced? Not merely separated but fully divorced.
1) Didnt Moshe Rabbeinu get divorced from Zipporah? See Rashi Bamidar 12:1,
2) Pirkei d’Rabbi Eliezer (chapter 30) brings down the following story that records that Yishmael divorced his wife.
3) (Sotah 12:a) is Amram who divorced Yocheved before remarrying her upon Miriam's advice. In fact, the Gemoro relates that the whole nation followed suit and divorced their wives. (Albeit, they [including Amram] all remarried soon after!)
4) King David's wife Queen Batsheva was previously married to Uriah. Uriah wrote a Get to her before he went to war so she should not be an Agunah if he were not to return. This Get came into effect at Uriah's demise, itself brought about by the King. (Kesubos 9:b)
The only divorce I can find in Tanach al pi peshat is Avraham's divorcing Hagar. The verse (Genesis 20:10) says:
The word used is גרש which is the word used for divorce generally in Tanach (eg. Leviticus 22:13) and it seems to be the peshat here because we never hear of Hagar again.
For what it's worth, pseudo-Jonathon explicitly interprets the verse: ופטרה בגיטא - and he exempted her with a document.