Temurah 23A

הכל מודים שאם משך אחת והקריבה שהשניה מתה, משכחת לה כגון שמשך אחת מהן והקריב, ודברי הכל.

All concede, even the Rabbis, that if the owner did not consult the court about which animal to sacrifice, but instead he took one of the animals and sacrificed it, he has demonstrated a lack of concern for the fate of the remaining animal, and that therefore the second animal is left to die. Consequently, you find that both clauses of the Mishnah are consistent with the opinion of the Rabbis, as one may interpret the latter clause as referring to a case where the owner took one of the two sums of money, used it to purchase an animal, and sacrificed the animal, and in such a case, all agree that the other sum of money is cast into the Dead Sea.

אלא לרבי אבא אמר רב, דאמר: הכל מודים במתכפר בשאינה אבודה ⁠— שאבודה מתה. על מה נחלקו? במתכפר באבודה, דרבי סבר: מפריש לאיבוד כאיבוד דמי, ורבנן סברי: לאו כאיבוד דמי.

But according to that which R' Abba says that Rav says, the Mishnah cannot be interpreted in this manner. As R' Abba said: All concede that in a case where one achieves atonement through the one that was not lost, the one that was lost is left to die. With regard to what case do the Rabbis and R' Yehuda HaNasi disagree? They disagree with regard to the case of one who achieves atonement with the one that was lost. As R' Yehuda HaNasi holds that if one designates a sin offering instead of one that was lost, it is considered like the lost sin offering. Accordingly, just as the lost animal is left to die if the second sin offering was sacrificed, the replacement animal is left to die if the original animal was sacrificed. And the Rabbis hold that if one designates a sin offering instead of one that was lost, it is not considered like the lost animal. Rather, if the original animal is sacrificed, the replacement animal is left to graze, as it was never lost.