What is the "judgement" of the 'Eed Al-Adhaa sacrifice that is made by a Muslim that is not praying? Is it Halaal or Haraam? Is it sufficient to say Bismillah Allaahu Akbar?

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. We ask Allaah to exalt his mention as well as that of his family and all his companions.

A person who does not perform prayers is of two kinds; there is a ruling that applies to each one, and this is discussed in Fatwa: 87319. As regards the sacrifice slaughtered by him whether or not it is acceptable, if he abandons the prayer while he denies its legitimacy, the sacrifice slaughtered by him is not accepted (because he is neither a Muslim nor from the People of the Book).

If a person abandons the prayer out of laziness, then his sacrifice is accepted according to the opinion of most of the scholars who do not consider him to be out of the fold of Islam. Nonetheless, to be on the safe side, it is better not to eat from the sacrifice slaughtered by him to avoid the difference of opinion of those who consider him as a disbeliever. However, if there is a greater benefit in eating from the sacrifice slaughtered by him like to soften his heart towards practicing Islam and the like, then it may be that it is more appropriate to eat from it in such a case, according to the opinion of most of the scholars.

Allaah knows best.