Answered by: Mufti Maruf Ahmed
What is the wisdom behind not shaving your beard or cutting your hair and nails before you give Qurbani on Eid-ul-Azha?
In the name of Allah, the Most Gracious, the Most Merciful
In the Hanafi Madh’hab, it is recommended to abstain from cutting hair or clipping nails during the first 10 days of Dhu’l Hijjah if one intends to perform Qurbani. However, it is not obligatory. 
Every matter in the religion is based upon wisdom, regardless of whether we understand or recognise them.
As for the wisdom behind avoiding clipping nails and cutting hair before sacrifice, the scholars have mentioned some possible reasons behind it.
Imam Nawawi (rahimahullah) states: “Our scholars have said that the wisdom for this is that when Allah Ta’ala grants salvation from Hellfire, every part of his body is included.”
Others have said that it is to imitate the pilgrims who are performing Hajj in the state of Ihram during these days. 
Only Allah knows best.
Written by Mufti Maruf Ahmed
Checked and approved by Mufti Mohammed Tosir Miah
Darul Ifta Birmingham
 Ibn Abideen: Radd al-Muhtar, vol. 6, pg. 407, Dar al-Kutub al-Ilmiyyah, Beirut, Lebanon
 Sharh Saheeh Muslim, vol. 5 pg. 120, Dar al-Fikr, Beirut, Lebanon
 Shawkani: Nayl Al-Awtar, vol. 6, pg 355, Dar Ibn al-Qayyim, Cairo, Egypt