Meat slaughtered by one who does not pray is not halaal, whether he says the name of Allaah over it or not. See question no. 70278.
With regard to saying Bismillah when slaughtering meat, the fuqaha’ differed concerning that and there are three points of view:
1 – That it is mustahabb only, which is the view of al-Shaafa’i.
2 – That it is a condition of the meat being halaal, but if a person forgets it by mistake it is still permissible. This is the view of the Hanafis, Maalikis and Hanbalis.
3 – That it is essential and cannot be waived under any circumstances, whether it is omitted by mistake or deliberately or out of ignorance. This is the view of the Zaahiris and was narrated from Maalik and Ahmad, and it was the view of some of the salaf; it was also the view favoured by Shaykh al-Islam Ibn Taymiyah. Shaykh Ibn ‘Uthaymeen (may Allaah have mercy on him) said: It is the correct view.
He also said: They quoted as evidence the general meaning of the verse in which Allaah says (interpretation of the meaning):
“Eat not (O believers) of that (meat) on which Allaah’s Name has not been pronounced (at the time of the slaughtering of the animal)”
And the Prophet (peace and blessings of Allaah be upon him) said:
“If the blood flows and the name of Allaah is mentioned, then eat.” So in order for the meat to be halaal, it is essential that the name of Allaah be mentioned. It is well known that if the condition is not met, the thing is invalid, so if the name of Allaah is not mentioned, the meat is not halaal, as with any other condition. Hence if a person prays but he forgot to do wudoo’, he has to repeat the prayer. Similarly if he prays not realizing that he had broken his wudoo’ because he thought that breaking wind does not invalidate wudoo’, or that eating camel meat does not invalidate wudoo’, for example, then he must repeat it, because the thing is not valid without the conditions being met. So if he slaughtered it but the blood did not flow, by mistake or out of ignorance, then it is not halaal, and the same applies if he does not mention the name of Allaah, because it is mentioned in the same hadeeth. End quote from al-Sharh al-Mumti’ (6/358).
See also: al-‘Inaayah Sharh al-Hidaayah (9/489); al-Fawaakih al-Dawaani (1/382); and al-Majmoo’ (8/387).
Based on this, he should not slaughter sacrifices or anything else unless he is one of those who pray regularly, and it is essential that he mentions the name of Allaah when slaughtering and says Bismillaah (in the name of Allaah).
It is also mustahabb to say takbeer, so he should say: Bismillaah, wa Allaahu akbar (In the name of Allaah and Allaah is Most Great).
Al-Bukhaari (5558) and Muslim (1966) narrated that Anas (may Allaah be pleased with him) said: The Messenger of Allaah (peace and blessings of Allaah be upon him) sacrificed two horned black and white rams. I saw him placing his foot on their sides, and he said the name of Allaah and he said takbeer, then he slaughtered them with his own hand.
And Allaah knows best.