In the famous Shakta Stotra, the Karpuradi Stotra, which was created by Lord Bhairava himself, it is mentioned that the Goddess loves sacrifice of animals including buffalo.
Sir John Woodroffe has a commentary on it and reference to this commentary is found in another book by the same author called "Shakti and Shakta". I am quoting from it.
Let us for the moment turn to the celebrated Hymn to Kali (of, as
those who read it might call, the extremist, that is Vira Shakta
worship) entitled the Karpuradi Stotra (Tantrik Texts,Vol. IX), which
like most (probably all) of its kind has both a material (Sthula) and
a subtle (Sukshma) meaning. In the 19th verse it is said that the Devi
delights to receive in sacrifice flesh, with bones and hair, of goat,
buffalo, cat, sheep, camel and of man. In its literal sense this
passage may be taken as an instance of the man-sacrifice of which we
find traces throughout the world (and in some of the Tantras) in past
stages of man's evolution. Human sacrifices permitted by other Semites
were forbidden by the Mosaic Code, although there is an obvious
allusion to such a custom in the account of the contemplated sacrifice
of Isaac by Abraham (Gen. xxii).
So, if we are to take this literally (on the gross level), then sacrifice of buffaloes are permitted in Devi worship. But we need to see the deeper spiritual (subtle) meanings embedded in such verses. Otherwise, the inquiry is never complete.
The same author writes in this regard the following:
Nothing is more common in all religions (and Christianity as by some
understood provides many examples) than to materially understand
spiritual truths. For such is the understanding of material of
Sthuladarshin (grossly seeing) men. But, even in the past, those who
were spiritual referred all sacrifice to the self; an inner sacrifice
which all must make who would attain to that Spirit which we may call
Kali, God, Allah, or what we will. But what is the Svarupa-vyakhya or
true meaning of this apparently revolting verse? The meaning is that
inner or mental worship (Antaryaga) is done to Her who is black
(Asita) because She is the boundless (Sita = Baddha) Consciousness
(Cidrupa) whose true nature is eternal liberation
(Nityamukta-Svabhava). And just as in outer worship material offerings
(Upacara) are made, so the Sadhaka sacrifices to Her his lust (the
Goat-Kama), his anger (the Buffalo-Krodha), his greed (the Cat-Lobha),
his stupidity of illusion (the Sheep-Moha), his envy (the
Camel-Matsaryya) and his pride and infatuation with worldly things
(the ManMada). All will readily recognize in these animals and man the
qualities (Guna) here attributed to them. It is to such as so
sacrifice to whom is given Siddhi in the form of the five kinds of
So, in the deeper level, sacrifice of buffalo is actually meant to be symbolic of "sacrificing our own anger", which is one of the many obstacles that arise in the spiritual path of the aspirant.
The following verses, from Mahanirvana Tantram's sixth chapter, can be added as reference too:
After worshipping (the Devi) with all the offerings, sacrifice should
be carefully made to Her (104). The ten approved beasts which may be
sacrificed are deer, goat, sheep, buffalo, hog, porcupine, hare,
iguana, and rhinoceros (105); but other beasts may also be sacrificed
if the worshipper so desires (106). The worshipper versed in the rules
of sacrifice should select a beast with good signs, and, placing it
before the Devi, should sprinkle it with the water from the
Vishesharghya, and by the Dhenu−Mudra should make it into nectar. Let
him then worship the goat (sheep, or whatever other animal is being
sacrificed) with (the Mantra) "Namah to the goat," which is a beast,
and with perfumes, flowers, vermilion, food, and water. Then he should
whisper into the ears of the beast the Gayatri Mantra, which severs
the bond of its life as a beast (107−108). The Pashu−Gayatri, which
liberates a beast from its life of a beast, is as follows: After the
word "Pashu−pashaya" say " Vidmahe," then, after the word
"Vishva−karmane," say "Dhimahi," and then "Tanno jivah prachodayat."
So, buffalo is one among the various animals that are approved for Bali (sacrifice).