Short answer
You can, and it is not a sin, but the sunnah is to eat nothing until after the Eid al-Adha prayer and to make your first food from your qurbani if possible. It is the opposite of Eid al-Fitr, where you eat before going. The four schools agree it is recommended.
Delaying eating until after the prayer on Eid al-Adha is mustahabb, whether or not you are sacrificing, according to the sounder view. Eating before it only leaves a recommended act; it is not makruh tahrimi.
The four schools agree on this.
Explanation
Buraydah reported that the Prophet ﷺ would not go out on the day of al-Fitr until he had eaten, and would not eat on the day of al-Adha until he had prayed. Scholars explain the difference: on Eid al-Fitr you show that the fast is over by eating early; on Eid al-Adha you wait to eat from the sacrifice, which comes after the prayer.
- Water, tea and medicine: drinking water or taking medicine is fine. Many scholars mention that the sunnah concerns food; if you need a coffee to function, it is not a sin.
- Children, the elderly and the sick: they eat as they need. The sunnah never requires harm.
- Diabetics: eat what your health requires and do not risk a low.
- Qurbani done abroad: you will not have its meat that morning. The sunnah of waiting until after the prayer still applies in the Hanafi school, so eat after you return.
- Late prayer times: if your mosque prays late, it is still better to wait if you can do so without difficulty.
The four schools agree on this recommendation, with small differences of wording about whether it is aimed especially at the one sacrificing. For the rest of the day's sunnahs, see what is Eid al-Adha, and for the prayer itself, how to pray Eid salah.
The evidence
Quran, Surah Al-Kawthar 108:2
فَصَلِّ لِرَبِّكَ وَٱنْحَرْ ﴿٢﴾
So pray to your Lord and sacrifice [to Him alone].
On this day prayer comes first, then the sacrifice.
Jami' at-Tirmidhi 542
Grading to be checked... لا يخرج يوم الفطر حتى يطعم ولا يطعم يوم الأضحى حتى يصلي ...
"He would not go out on the day of al-Fitr until he had eaten, and would not eat on the day of al-Adha until he had prayed."
The sunnah is to delay eating on Eid al-Adha until after the prayer.
Where the ruling is recorded
- al-Durr al-Mukhtar, Kitab al-Salah, chapter on the two Eids. Delaying eating on al-Adha is recommended even for one not sacrificing, and eating first is not makruh.
- Nur al-Idah with Maraqi al-Falah, Chapter on the two Eids. Lists not eating before the al-Adha prayer among the sunnahs.
Checked by our team. For a more accurate answer to your own situation, consult a scholar. Quran translation by Sahih International. Hadith Arabic from the standard editions of the six books and the Muwatta, with gradings as recorded there; the English is our own rendering. Spotted a mistake? Tell us.