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.
In principle, the meat of animals slaughtered by the People of the Book is lawful if it is predominantly thought that it is slaughtered according to Islamic rites, which is cutting the throat and the gullet, or the throat and the two jugular veins according to another opinion of the scholars. This is the Islamic method of slaughtering.
As regards cutting along the neck, then this is not an Islamic way of slaughtering; however, if you mean that this is done after the slaughtering according to the correct method takes place and the soul of the animal leaves the body, then this method of cutting is permissible.
With regard to knocking the animal in the head and doping and electrocuting it, then if this does not kill the animal and it is later slaughtered according to Islamic rites, then this does not affect the Islamic method of slaughtering. The Fiqh Committee resolution reads:
"It is not forbidden to slaughter the animal according to Islamic rites after having doped it with the use of a mixture of CO2 and O2 or by using the captive bolt pistol in a way that this does not cause its death before slaughtering it according to Islamic rites.”
However, if that method leads to the death of the animal before it is slaughtered according to Islamic rites, then in this case it is considered as dead meat and it is not permissible to eat it.
For more benefit, please refer to Fataawa 82323, 82065 and 81234.
To conclude, if a Muslim knows that the slaughtering takes place according to Islamic rites, then he may eat from the animal slaughtered by the People of the Book, but if he does not know the method of slaughtering, he may also eat from it according to the principle if the slaughtering according to Islamic rites is predominant (in that country). However, if he doubts the method of slaughtering or that the people of that country kill the animal and they do not slaughter, then in this case it is not permissible for him to eat from it because the rule is in accordance with the widespread norm. The Prophet said: “Leave that which you doubt about to that which you do not doubt about.” [Ahmad and An-Nasaa’i] Therefore, a Muslim should seek to eat lawful and good food.