This excerpt is taken from Sheikh Farooq Rafi Sahib's book Qurbani, Aqiqah, and Ashra Zil-Hijjah.
Prohibited Animals in Sacrifice:
It is necessary that the sacrificial animals be free from the following defects, and the sacrifice of an animal afflicted with any of these defects is not permissible:
① An animal that is deaf with obvious deafness.
② A sick animal with a clear illness.
③ A lame animal with evident lameness.
④ An extremely thin animal whose bones have no flesh left.
⑤ An animal with cuts, tears, or holes in its ears.
⑥ An animal with more than half of its ear cut off or more than half of its horn broken or cut.
Ubaid bin Firoz, may Allah have mercy on him, narrates that I asked Sayyiduna Bara bin Azib, may Allah be pleased with him, which animals' sacrifice is not permissible? He said that the Messenger of Allah, peace and blessings be upon him, stood among us (for a sermon), although my fingers are smaller than the fingers of the Messenger of Allah, peace and blessings be upon him, and the joints of my fingers are smaller than the joints of his fingers, (he indicated with his fingers) and said:
أربع لا تجوز فى الأضاحي، العوراء بين عورها، والمريضة بين مرضها، والعرجاء بين ظلعها، والكسير التى لا تنقي
"Four types of animals' sacrifice is not permissible: ① A deaf animal whose deafness is apparent. ② A sick animal whose illness is clear. ③ A lame animal whose lameness is evident. ④ And an extremely weak, thin animal whose bones have no flesh."
Reference: Sahih: Sunan Abi Dawood, Kitab al-Dahaya, Bab Ma Yukrah min al-Dahaya: 2802. Jami' at-Tirmidhi, Abwab al-Adhahi, Bab Ma La Yajooz min al-Adhahi: 1497. Sunan an-Nasa'i, Kitab al-Dahaya, Bab Ma Nahi 'anhu min al-Adhahi: 4374. Sunan Ibn Majah, Abwab al-Adhahi, Bab Ma Yukrah an Yudhha bihi: 3144. Musnad Ahmad: 289/4. Sahih Ibn Khuzaymah: 2912. Sahih Ibn Hibban: 5919
Benefits:
Imam Nawawi, may Allah have mercy on him, states:
وأجمعوا على أن العيوب المذكورة فى حديث البراء وهو المرض والعجف، والعور، والعرج البين لا تجزئ التضحية بها، وكذا ما كان فى معناه أو أقبح كالعمى وقطع الرجل وشبهه
“The scholars have consensus on this issue that the sacrifice of animals afflicted with the mentioned defects, namely obvious disease, extreme thinness, apparent deafness, and apparent lameness, is not valid. Similarly, the sacrifice of animals afflicted with these defects and even more severe defects, such as blindness and a cut leg, is also impermissible.”
Reference: Sharh al-Nawawi: 12/13. Subul al-Salam: 1356/4
Minor defects are not worthy of consideration:
Minor defects in sacrificial animals, less severe than the mentioned defects, do not invalidate the validity of the sacrifice, and it is permissible to sacrifice animals with minor and non-apparent defects.
① Amir San'ani, may Allah have mercy on him, says:
والحديث دليل على أن هذه العيوب مانعة من صحة التضحية، وسكت عن غيرها من العيوب، فذهب أهل الظاهر إلى أنه لا عيب غير هذه الأربعة وذهب الجمهور إلى أنه يقاس عليها غيرها مما كان أشد منها أو مساويا لها كالعمياء ومقطوعة الساق
"This hadith is evidence that the mentioned defects prevent the validity of the sacrifice, and for other defects besides these, silence has been maintained. Accordingly, the apparent scholars hold the view that no defect other than these four defects invalidates the permissibility of the sacrifice. However, the majority of scholars hold the view that defects more severe than the mentioned ones and similar defects, such as the sacrificial animal being blind or having a cut leg, etc., will also be analogized to the mentioned defects."
Reference: Sabil al-Salam: 1356/4
② Khattabi, may Allah have mercy on him, states:
في الحديث دليل على أن العيب الخفيف فى الضحايا معفو عنه ألا تراه يقول بين عورها بين مرضها، بين ظلعها، فالقليل منه غير بين، فكان معفوا عنه
"The hadith of the chapter is evidence that minor defects in sacrificial animals are excused, and you do not see that the Prophet, peace be upon him, mentioned defects of the sacrifice except that its deafness is apparent, its disease is clear, its lameness is evident, so defects less than these are not apparent and are excused."
Reference: A'un al-Ma'bud: 18/8