The laws of kosher slaughter must be performed by or under the supervision of a competent person. The knife must be smooth so as to spare the animal pain.

1:1 All may slaughter and what they slaughter is valid, except a deaf-mute, an imbecile, and a minor, lest they incorrectly slaughter. But if any of these slaughtered in the presence of others, what they slaughtered is valid. Whatever is slaughtered by Gentiles is carrion,¹²⁷ and it transmits impurity by being carried.¹²⁸ One who slaughtered at night, and in the same way a blind man who slaughtered, what he slaughtered is fit. One who slaughtered on the Sabbath or on the Day of Atonement, although he is liable for his life, what he slaughtered is fit.

1:2 One who slaughtered with a hand sickle, flint, or reed, what he slaughtered is fit. All may slaughter at any time and with any implement except a scythe, a saw, teeth, or fingernails, since these choke the animal by mangling the windpipe rather than cutting it. One who slaughtered with a scythe, drawing the blade backwards, the House of Shammai declares it unfit, but the House of Hillel declares it fit. If the teeth of the scythe are filed down, then it is like a knife.

The Mishnah also specifies the exact requirements in the separation of milk and meat as understood to be prohibited by the Torah.

8:1 No meat may be cooked in milk, except the meat of fish and locusts.¹³⁰ No meat may be served on the table with cheese except the meat of fish and locusts. One who vowed to abstain from meat may eat the meat of fish and locusts. Fowl may be served at the table together with cheese, but may not be eaten with it. This is according to the School of Shammai. But the House of Hillel say it may not be served or eaten with it.¹³¹ Rabbi Yose said: This is one of the lenient rulings of the House of Shammai, and one of the strict rulings of the House of Hillel. What kind of table did they refer to? A table at which people eat. But on a table upon which food is only set out one may put one beside the other without concern.

8:2 One may tie up meat and cheese in the same cloth so long as they do not touch each other. Rabban Simeon ben Gamliel said: “Two guests who are strangers may eat at the same table, one meat and one cheese, without concern.”¹³²

8:3 If a drop of milk fell upon a piece of meat cooking in a pot, and there was enough to give flavor to that piece, it is forbidden. If one stirred the pot and there was enough to give flavor to the whole pot, it is forbidden. One should cut open the udder and empty out the milk, but if he has not cut it open, he has not transgressed. He should cut open the heart and empty out the blood, but if he has not cut it open, he has not transgressed. If one served fowl and cheese on the table together, he has not transgressed a negative commandment.¹³³

8:4 It is prohibited to cook or derive any benefit from the meat of a clean (kosher) animal with the milk of a clean animal. It is permitted to cook or derive benefit from the meat of a clean animal with the milk of an unclean animal, or the meat of an unclean animal with the milk of a clean animal.¹³⁴ Rabbi Akiva says: “Wild animals and birds are not prohibited by the Torah, for it is written three times, ‘You shall not seethe a kid in its mother’s milk’ (Exod. 23:19; 34:26; Deut. 14:21), excluding wild animals, birds, and unclean animals from this prohibition.”¹³⁵

Rabbi Yose the Galilean says: “It is said, ‘You shall not eat carrion’ (Deut. 14:21), and it is said, ‘You shall not seethe a kid in its mother’s milk.’ Whatever is forbidden under the law of carrion, it is forbidden to seethe in milk. One might think that a bird, which is forbidden under the law of carrion, is forbidden to be seethed in milk. Thus, the verse says, ‘in its mother’s milk,’ a bird is excluded since it has no mother’s milk.”¹³⁶

129. Trans. S. Berrin
130. Only the meat of animals and fowl (the latter by Rabbinic ordinance) must be separated from milk.
131. This was the ruling adopted by the Talmud as law.
132. Since they are strangers there is no concern that they may share their food.
133. But it was prohibited by Rabbinic ordinance.
134. Despite the fact that such a mixture may not be eaten.
135. The prohibition of eating these animals with milk would therefore be Rabbinic.
136. Nonetheless, the Rabbis ruled that it was forbidden to eat fowl with milk because of the similarity of fowl to meat.