Kerisos, chapter 6, mishnah 7. The topic of this mishnah and the following mishnah is a situation where a person sets aside an animal or money for a specific offering, and the fundamental question underlying them is: to what extent is the designation fixed, and to what degree is it possible to transfer the designation to a different purpose.
Our mishnah establishes that regarding a chatas, one who designates an animal for a chatas - it must be for that same person and for that specific sin. Three cases are brought here:
A father who designated and a son who inherited: A father who designated an animal as a chatas for his sin and died without bringing it, and his son inherits all his property, including this animal - the son cannot bring it for his own sin. Even if the father and son desecrated Shabbos together at the exact same time, since the father designated it for his own sin, the son is not permitted to use it for his own sin.
Two different sins: A person who ate chelev and said "this shall be my chatas for the chelev I ate inadvertently," and later that day ate blood - he cannot bring the animal he designated for the chelev for the transgression of blood.
The same sin at two times: He ate chelev and designated an animal, and the next day ate chelev again - he cannot bring the animal he designated for yesterday's transgression for the sin he committed today. A new animal is required, and it cannot be switched at all.
The source of the law:
The basis of this is a verse, which teaches that the specific offering was designated for a specific sin. From this, it emerges that in the first two cases there is no possibility at all to use the animal: a son who brings his father's animal for a chatas - as they are not the same person; and the father himself cannot transfer it from chelev to blood or vice versa - as it is not the same sin.
The third case, that a person is not permitted to bring the animal he designated for eating chelev yesterday for eating chelev today, is a rabbinic law, and is not based on the verse. Because from the Torah, it is the exact same person and the exact same sin, chelev for chelev. But the Sages said that in order that people not come to confusion, one should not transfer it even from one sin to another sin of the same type.
Let us turn to the text of the mishnah:
"Hamafrish chataso umeis" - a person who designates an animal for a chatas and says: This goat shall be my chatas for the desecration of Shabbos that I committed, and afterwards dies. As we learned in tractate Zevachim (page 10), this is one of the five cases of 'chataos that die' - an animal designated for a chatas that cannot be offered, and is left to die. However, our mishnah is not dealing with them.
Our mishnah focuses on another animal: "Lo yevi'ennah" - he may not bring it. For example: a person who desecrated Shabbos and also ate on Yom Kippur. For desecrating Shabbos he designated a first goat, and for eating on Yom Kippur he designated a second goat. He comes to the Temple and brings them to the kohen, and says: "I owe two chatas offerings, one for Shabbos and one for Yom Kippur, and here are the goats."
The mishnah teaches that the kohen asks: which goat is for Shabbos and which is for Yom Kippur? And the person cannot say: "What does it matter? They are two goats, two chataos, and they should be offered together." That does not work. Specifically the goat that was designated for Shabbos is offered for Shabbos, and the goat that was designated for eating on Yom Kippur is offered for eating on Yom Kippur. This is the point of our mishnah.
And a third point: Even regarding chelev that he ate last night, he cannot bring the animal he designated yesterday for yesterday's transgression, even for the exact same transgression committed today. The animal is designated for that specific transgression as it was set aside for it.
The basis for this is in the verse (Leviticus 4:28): "Korbano al chataso" - the designated offering must be his own offering and for his specific sin that he designated it for, and not for another sin, and not for another person.
In summary: In the first two cases - a son who brings for his own sin the animal he inherited from his father which had been designated in advance for his father's sin, and a father who brings an animal he designated for one sin for another sin - both laws are d'Oraisa, and are based on the verse, "his offering for his sin." However, the third halachah in our Mishnah, that even for the exact same sin, such as desecrating Shabbos on two consecutive weeks, a person may not bring the animal he designated last week for the Shabbos desecration of this week - is d'Rabbanan, lest he become confused and come to violate one of these two d'Oraisa laws.