Praise be to Allah.
Swearing by anything other than Allaah, such as the Ka’bah or the Prophet (blessings and peace of Allaah be upon him) or any righteous person or by the head of so and so or by the honour of so and so -- all of that is shirk, as it says in the saheeh hadeeth: “Whoever swears by anything other than Allaah has committed shirk.” and the Prophet (blessings and peace of Allaah be upon him) said: “Do not swear by your fathers or by the rivals (of Allaah), and do not swear by Allaah unless you are speaking the truth.”
If a person swears by anything other than Allaah, he is not obliged to fulfil his oath, because it is an oath that is not to be honoured. The words of the questioner are general and open to different interpretations. If you meant what I have mentioned above, then he is not obliged to do anything, whether it is offering expiation or anything else, and he is not obliged to go ahead with the divorce. But if what the questioner meant was swearing to divorce, such as saying: If you speak to so and so, then you are divorced, or If I do such and such, then my wife is divorced -- this is a matter concerning which the scholars differed. Some of them say that divorce takes place for the one who breaks this oath. Some of them say that if the intention of the one who swears the oath is to prevent himself or someone else from doing a certain action, or encouraging a certain action, then his divorce does not take place and he has to offer expiation. This is the view which was approved of and favoured by Shaykh al-Islam Ibn Taymiyah (may Allaah have mercy on him), and it has been expressed in fatwas by many of the modern scholars, including our Shaykh, ‘Abd al-‘Azeez ibn Baaz (may Allaah have mercy on him). And Allaah knows best. May Allaah send blessings and peace upon our Prophet Muhammad.