Mishnah/Seder Kodashim/Tractate Kinnim/Chapter 1/3
Seder Kodashim, Tractate Kinnim: Chapter 1, Mishnah 3
In the Vilna edition of the Mishnah, this text is presented as mishnah 2. The mishnah 3 of the Vilna edition appears here as mishnah 4.
Hebrew Text 
- חטאת שנתערבה בעולה,
- ועולה בחטאת,
- אפילו אחת בריבוא – ימותו כולם.
- חטאת שנתערבה בחובה,
- אין כשר אלא מניין חטאות שבחובה.
- וכן עולה שנתערבה בחובה,
- אין כשר אלא מניין עולות שבחובה.
- בין שהחובה מרובה ונדבה מועטת,
- בין שהנדבה מרובה וחובה מועטת,
- בין ששתיהן שוות.
English Translation 
- [In the case of] a sin-offering which became mixed in with elevation-offering[s],
- or an elevation-offering [which became mixed in] with sin-offering[s],
- even one in ten thousand – they must all be put to death.
- [In the case of] a sin-offering which became mixed in with obligatory [pairs],
- only the number of sin-offerings among the obligatory [pairs] are permitted [to be sacrificed].
- Similarly, [in the the case of] an elevation-offering which became mixed in with obligatory [pairs],
- only the number of elevation-offerings among the obligatory [pairs] are permitted [to be sacrificed].
- [The above is true] whether the obligatory [pairs] are many and the donated [elevation-]offering[s] are few,
- whether the donated [elevation-]offering[s] are many and the obligatory [pairs] are few,
- [or] whether they are both equal.
They must all be put to death 
Once animals have been consecrated to be sacrificed in the Temple, they are not permitted to be used for any other purpose, or to be sold.
When sin-offerings and elevation-offerings have become mixed, it is also impossible to sacrifice them properly, since it is forbidden to perform the service for a sin-offering on an elevation-offering, and vice versa. These animals have the status of sacrifices which cannot be offered, and are put to death in an indirect fashion. This is done out of the concern that if the animals were to sit around for many years, they would eventually be mistakenly or unintentionally used by someone for personal benefit. To derive even a nominal benefit from items sanctified to God is the grave sin of me'ilah. (See Tractate Meilah)
Only the number of sin-offerings among the obligatory pairs are permitted to be sacrificed 
Since obligatory bird-pairs consist of one sin-offering and one elevation-offering, up to half of those birds (the "number of sin-offerings...") may be offered as sin-offerings, and the other half will by default be considered the elevation-offerings of the set. These elevation-offerings may not be sacrificed according to the service of a sin-offering. Therefore, no further birds from the mixture may be brought as sin-offerings, out of the concern that the bird is one of these elevation-offerings.
Also, none of the birds whatsoever can be brought as elevation-offerings, out of the concern that the bird is the sin-offering which became mixed in.