Tosafos on Amud Aleph (“Rava”) discusses the possibility that an ox or donkey which was used in the sinful acts of either plowing together (which is a forbidden mixture, Devarim 22:10) or threshing while muzzled (ibid, 25:4) would be invalided to use as a sacrifice. The Keren Orah asks in regard to the scenario of threshing with a muzzle, but the action of the threshing itself was not a sin. That is, the ox did not participate in this action  as it was merely muzzled.  This is unlike an animal that plowed as part of the forbidden mixture, where the animal itself did the sinful act of plowing.  In that case, the act of plowing along with a different non-matched animal is understood as a discrete sinful act.  The action itself is different when done in tandem with the unequal force of a mismatched partner animal. However, threshing is the same threshing with or without a muzzle, and the locus of the sin should be the muzzle, not the animal. Why would the animal be rendered invalid?  

(I can’t resist commenting:  This basic decency which the Torah demands toward an animal, that we are forbidden to make it work when muzzled, was deprived of school age children for more than a year due to what seems to me to have been unreasonable COVID caution and hysteria.)

In any case, back to the Keren Orah’s question. The simplest answer might be that Tosafos referenced a cluster of related prohibitions, but didn’t specifically mean muzzling. However, a deeper answer is that Tosafos considered the act of threshing while muzzled as intrinsically sinful, and the locus of the sin resides in the ox, making it invalid for a sacrifice. How can we conceptualize this?

Actually there is a depth of Kabbalistic meaning construed from the verses describing this prohibition. Recanti (Ki Tetze, 25) notes the proximity of the verses prohibiting muzzled threshing and levirate marriage. As alluded to by Rishonim such as Ramban, the Levirate marriage is built on the principle of reincarnation. (See Psychology of the Daf, Yevamos 2.) Chizkuni reads into the homophonic similarity of the word “shor”=“ox” to “shir”=“song”. This ox is actually a reincarnated human soul who is suffering the punishment for having sung licentiously in a mixed group. So now he is made to “sing” as he threshes. The owner must regard this process to allow for this soul’s expiation, and so the ox should not be muzzled. 

In a different manner, Chasam Sofer (Ki Tetze) also reads a mystical process into this prohibition, though very different. There seems to be a genuine theological idea that we give the devil its due. That is, certain Jewish rituals enact a degree of giving recognition to the evil forces and not fully rejecting them. As examples, he cites the sacrificial goat that is designated for Azazel, the fact that the verse states 40 lashes but we never give more than 39, as well as the idea of a feast over a mitzvah. Each of the rituals express recognition of the potencies of evil. The goat offering to Azazel is a strange and most difficult to understand example of a Jewish sacrificial ritual involving appeasement of evil forces (see Ibn Ezra and Ramban Vayikra 16:8, and Psychology of the Daf Yoma 15.) The person is not given 40 lashes, but only 39, to note that the evil cannot be fully expunged.  Celebrating a mitzvah, which is a spiritual matter by indulging in a physical feast, is another example of this according to the Chasam Sofer. Lastly, giving the ox its allotted portion of food while threshing, is symbolic of allowing the satanic ox a tribute by being able to eat by threshing. (I am not sure why the ox is a symbol for something satanic, but perhaps it just represents brute physicality.) 

On the surface, these ideas sound idolatrous and not Jewish. However, some mystical concepts do seem that way, and that is probably one of the reasons that access to them are restricted to the novice, as they can be misread in a heretical manner. I’m no mekubal, but I do often sense psychological meaning in kabbalistic ideas, and I even sometimes wonder if they are saying the same thing but expressing it in a different kind of language. There is an intuitive truth to the notion that we cannot fully fight or expel evil, because every part of our personality is us. We need to modulate and work with all our parts in the correct proportion. That is why the Hebrew word for character trait is “middah”, which literally means “measure”. This is because all parts of a person are neither truly evil nor good; what matters is that the proportion be correct. Other teachings within our tradition also speak of this idea that evil has its place. For example, the famous Gemara in Yoma (69b) where the Men of the Great Assembly succeeded in capturing and containing the “evil inclination” only to discover that “all chickens stopped laying eggs”, that is all reproductive urges ceased. Or the teaching in Sotah (47a) that “one should push off his Yetzer Hara with his left hand, while pulling closer with the right.” This also suggests a realistic recognition of the value of certain instincts and drives that are labeled evil, but in proportion serve a purpose.

Getting back to the Keren Orah. If we take these mystical explanations of the prohibition against muzzling while threshing into account (however poorly we might make sense of them), it is easier to understand how the act can taint the ox and invalidate it as a sacrifice. If the ox’s expiation was thwarted by muzzling according to Recanti, then the ox is now invalidated. And according to Chasam Sofer, if the evil forces are not properly mollified, it also makes sense that this ox is tainted and cannot be used.

One final point, even though Recanti and Chasam Sofer were saying completely different ideas, It is too much of a coincidence that this verse specifically attracted mystical attention and focus, as opposed to many others. My hunch is that just as certain words in the Torah are predisposed by tradition to be open to Gezeirah Shava (Pesachim 66a), so too perhaps there was a common mystical tradition about certain verses being open to esoteric meaning. Especially because esoteric teachings were by innuendo and cryptic, and forbidden to be stated outright (see Chaggigah 13a), one master’s hints at significance in a verse could be interpreted by his disciples in a variety of ways.