I have been living in the U.S for over 20 years and have been fighting this war of "Zabiha Meat" with lot of people. My question is that can I buy beef, for example, from average market which was never prepared or prayed upon by Muslim slaughter way? People argue that in Al-An'am it clearly says: Eat not of (meat) on which Allah's name hath not been pronounced: That would be impiety. But the evil ones ever inspire their friends to contend with you if you were to obey them, you would indeed be Pagans." (Q. 6:121) Therefore, meat has to be prayed upon by Muslim with Allah's name before it can be eaten by Muslim.
The Almighty Allah has allowed the believers only to consume the flesh of the animals which are slaughtered while invoking Allah's name. If an animal is not slaughtered the prescribed way or God's name has not been invoked while slaughtering or it has been slaughtered by invoking the name of other than God then it is not allowable. For detail please refer to: http://www.al-mawrid.org/pages/articles_english_detail.php?rid=357&cid=452