The Mishnah taught (Daf 15-1 (c)) that R. Yehuda permits selling them injured large animals.

R. Yehuda was only discussing a blemish that cannot heal. (Since it cannot be used for working the land, it is assumed that the idolater will slaughter it, so there is no concern that another Jew will see the animal formerly owned by the Jew in the house of the idolater and assume that is permitted to sell even an uninjured large animal to an idolater.)

Question (Chachamim to R. Yehuda): But the idolater might leave the cow alive in order to bring a male to mate with it?

Answer (R. Yehuda to Chachamim): I was only discussing a male horse that cannot heal.

Question (Chachamim to R. Yehuda): Why wouldn't the idolater keep the male horse alive in order to bring a female and mate them for their offspring?

(R. Avin citing Rabbanan of Bavel): This shows that it is prohibited to sell fetuses of animals to idolaters (lest they keep them and work them when they have fully grown).

(Mishnah in Maseches Bechoros): One who transgresses and buys the offspring of an idolater's donkey or one who sells one to him; one who partners with him and one who receives one from him to rear and one who gives it to an idolater to rear, in all these cases, it is exempt from the laws of the firstborn.

Question (R. Chagai to R. Yosi): Doesn't he say that one may not sell fetuses of an animal to an idolater?

Answer (R. Yosi): R. Avin has already preceded you by saying in the name of the Rabbanan of Bavel, that there is proof that even R. Yehuda agrees that one may not sell fetuses of animals to a gentile.

The Mishnah (15-1 (d)) taught that Ben Beseirah permits selling them a horse.

Ben Beseirah was only speaking about a male horse because it kills its owner in battle.

(How does it kill its owner in battle?) Some say that it chases after a female horse of the enemy; some say that it stops to urinate.

What is a practical difference between these two opinions?

If it is neutered - it will not chase after a female, but it will stop to urinate.

(R. Tanchum bar Chiya): (The reason that the Chachamim disagree with Ben Beseirah and prohibit selling them a horse, is that) when it becomes old, it can still be used to turn the millstones and grind flour.

(R. Yosi bei R. Bun citing Rav Huna): Ben Beseirah and R. Nasan both said the same thing - as the Beraisa teaches -

On Shabbos, if a person took out into a public domain a domesticated animal, or a wild animal or a bird, whether alive or dead, he is liable. R. Nasan said that he is exempt for a live one (because a living being carries itself).

Question: Why did the Rabbanan respond to Ben Beseirah that an elderly horse can also be used for sin as it can still be used to turn the millstone? Surely according to the Rabbanan, a horse that carries birds will also be prohibited to sell, since they do not reason that a living being carries itself?

Answer: They responded to Ben Beseirah according to his own opinion. According to you, who reasons that a horse that carries a bird only involves a Rabbinic prohibition, nevertheless, there could be a Torah prohibition if it grinds flour.

(Rebbi): I say that it is prohibited to sell a horse to an idolater - because he will use it is a weapon to kill and because it is a large animal that will be used for work on Shabbos.

Question: (The next Mishnah teaches that one may not sell a dangerous animal to an idolater that may cause public damage. This implies that if they do not cause public damage, it is permitted.) But doesn't the Tosefta teach that a large beast is like a large animal (that it may never be sold to an idolater)?

Answer: The Tosefta follows the opinion of Rebbi, but as for the Chachamim, R. Bisna/ R. Chanan bar Ba said in the name of Rav that a large beast is like a small animal, about which there are varying customs as to whether they may be sold to an idolater or not.