Uthman bin Abi Sulayman said that Safwan bin Umayyah (may Allah be pleased with him) said: The Messenger of Allah (peace and blessings be upon him) saw me taking the meat off the bone with my hand, and he (peace and blessings be upon him) said: "O Safwan!" I said: "O Messenger of Allah! At your service." He said: "Bring the meat close to your mouth, for it is more wholesome and more pleasant."
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصداق / 14625
Sayyidah Aishah (may Allah be pleased with her) said that the Messenger of Allah (peace and blessings be upon him) said: "Do not cut meat with a knife, for that is the practice of the non-Arabs; rather, bite it off the bone, for it is more wholesome and easier to digest."
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصداق / 14626
Sayyiduna Amr bin Umayyah (may Allah be pleased with him) saw the Messenger of Allah (peace and blessings be upon him): the Prophet (peace and blessings be upon him) was cutting meat from the shoulder of a sheep and eating it. When the call to prayer was given, he put down the meat and the knife. Then he (peace and blessings be upon him) prayed and did not perform ablution.
Note: This hadith indicates that cutting with a knife is permissible. If the previous hadith is authentic, then tearing it off with the teeth is better.
Hadith Referenceالسنن الكبرى للبيهقي / كتاب الصداق / 14628