All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah, and that Muhammad is His slave and messenger.
First of all, it should be noted that a Muslim should not be excessive in making oaths. The evidence for this is that Allaah Almighty says (what means): {...But guard your oaths. Thus does Allaah make clear to you His verses that you may be grateful.}[Quran 5:89] The frequent making of oaths weakens the sense of Allaah's Greatness and the fear of Allaah in one's heart, and this is among the most dangerous things that can happen to a person, as it results in the person committing sins easily and being negligent regarding performing acts of worship.
Nonetheless, you should know that if a person makes oaths to do different things, he is obliged to put forth expiations for all the oaths that he broke, and it does not suffice to offer a single expiation for all the oaths he has broken.
If a person makes an oath to do only one thing, or to leave something, even if he breaks his oath many times, he is only required to expiate once if he did not expiate for the same oath before. However, if he expiated for the oath he has broken and then he makes an oath to do/leave the same thing again and breaks it, then he is obliged to expiate a second time, and so forth.
If a person does not know the number of oaths that require expiation, then he should endeavor to find out its number [by estimating it], and if he cannot know this, he should expiate for such a number of oaths that he believes they are most likely to be sufficient for clearing himself of liability.
To learn more regarding the expiation of oaths, please refer to Fataawa 11288 and 87181.
On the other hand, keeping a beard is an obligation as underlined in Fataawa 82143 and 81533. Indeed, keeping a beard is more emphasized in your case given the oath you have made.
Since, you did not keep your beard completely as was required from your oath, then you have broken your oath and you are required to offer expiation for it.
Allaah Knows best.