NOTE. Śrīla Rāmānujācārya describes Vedic animal sacrifices in his commentary to Bhagavad-gītā 2.31 thus:

agnīṣomīyādiṣu ca na hiṁsā paśoḥ nihīnatara-cchāgādi-deha-parityāga-pūrvaka-kalyāṇa-deha-svargādi-prāpakatva-śruteḥ saṁjñapanasya. na vā u vetan mriyase na riṣyasi devāṉ ideṣi pathibhiḥ sugebhiḥ. yatra yanti sukṛto nāpi duṣkṛtas tatra tvā devaḥ savitā dadhātu iti hi śrūyate [...] ataḥ cikitsaka-karma āturasya iva asya rakṣaṇam eva agnīṣomīyādiṣu saṁjñapanam.

“In the Agnīṣomīya and other such sacrifices, no injury is done to the animal sacrificed, for the Śruti declares that the sacrificed animal abandons its inferior body like that of a goat and attains an auspicious body in svarga and so on.¹ Indeed, the Śruti says, ‘(O sacrificial animal), by this act (of sacrificing you), you never die at all; you are not killed. You will go through blissful paths to the devas where only the pious, and not the sinful, reach. And may the sun-god establish you there!’ (Taittirīya Brāhmaṇa 3.7.92) [...] Hence, just as lancing and such other operations of a surgeon are for the protection of a suffering patient, the killing of the sacrificial animal in Agnīṣomīya and other such sacrifices is only for its protection.”

In his Śrī-bhāṣya commentary on Vedānta-sūtra 3.1.25, he also states:

paśor hi saṁjñapana-nimittāṁ svarga-loka-prāptiṁ vadantaṁ śabdam āmananti: “hiraṇya-śarīra ūrdhva-svargaṁ lokam eti” ityādikam. atiśayitābhyudaya-sādhana-bhūto vyāpāro ’lpa-duḥkho ’pi na hiṁsā. pratyuta rakṣaṇam eva [...] cikitsakaṁ ca tādātvikālpa-duḥkha-kāriṇam api rakṣakam eva vadanti pūjayanti ca taj-jñāḥ.

“The Śruti declares that the killing of sacrificial animals makes them to go up to the heavenly world, and therefore is not of the nature of violence. This is declared in the text, ‘With a golden body it ascends to the heavenly world.’ An action which is the means of great elevation is not violence, even if it involves some little pain; it rather is of beneficial nature [...] An act of healing, although it may be the cause of immediate temporary pain, is preservative and beneficial. Those who know the nature of sacrifice declare so and worship such an act.”²

Śrīla Madhvācārya quotes from the Varāha Purāṇa in his commentary on the above-mentioned Vedānta-sūtra as follows:

hiṁsā tv avaidikā yā tu tayānartho dhruvaṁ bhavet
vedoktayā hiṁsayā tu naivānarthaḥ kathañcana

“Non-Vedic violence certainly leads to undesirable consequences. But through violence taught in the Vedas there are no undesirable consequences whatsoever.” ³

Ācārya Baladeva Vidyābhūṣaṇa sheds further light in his commentary on this sūtra as under:

dharmatvādharmatvayor vedaika-gamyatvād vedenaiva hiṁsā-anugraha-ātmakasya iṣṭāder dharmatvāvadhāraṇān nāśuddhaṁ tad iti. na ca mā hiṁsyād iti niṣedhāt pāpaṁ hiṁseti vācyam. utsargo hi saḥ. agnīṣomīyam iti tv apavādaḥ. utsargāpavādayor vyavasthita-viṣayatvāt na kiñcic codyam asti.

“Dharma and adharma can only be known through the Vedas, and we understand that the Vedas themselves prescribe certain animal sacrifices and so such sacrifices are to be understood to be dharma and not impure. One cannot claim that it is not so because the Vedas prohibit animal sacrifices by stating “Do not harm anyone” for this is a general injunction whereas the injunction ‘One should sacrifice an animal dedicated to Agni and Soma’ is an exception. Since general injunctions and exceptions have distinct scopes of application, there cannot be any objection to such animal sacrifices.”⁴

Commentaries on this sūtra by Śrīla Nimbārkācārya’s followers contain some of the above points.

In Caitanya-caritāṃrta (Ādi 17.164), we find Lord Śrī Caitanya Mahāprabhu explaining that Aśvamedha sacrifices are forbidden in Kali-yuga:

aśvamedhaṁ gavālambhaṁ sannyāsaṁ pala-paitṛkam
devareṇa sutotpattiṁ kalau pañca vivarjayet

“In this Age of Kali, five acts are forbidden: the offering of a horse in sacrifice, the offering of a cow in sacrifice, the acceptance of the order of sannyāsa, the offering of oblations of flesh to the forefathers, and a man’s begetting children in his brother’s wife.”⁵