Pesachim, Chapter 5, Mishnah 4. The Torah states: "Lo sishchat al chametz dam zivchi" - one may not slaughter the korban Pesach while chametz is still in one's possession. Our Mishnah deals with the scope of this prohibition: which services it applies to, to whom it applies, and at which times.
The scope of the prohibition:
The services: Our Sages derived that the prohibition is not limited to the slaughtering alone, but applies to each of the primary services of the korban Pesach: receiving the blood, sprinkling the blood, and burning the eimurim.
Whose chametz: It is not required that the chametz specifically belong to the one performing the service; it is enough that the chametz is in the possession of any one of the members of the group registered for that korban Pesach.
The punishment: One who performs the service at that time receives lashes, for having transgressed the prohibition of "Lo sishchat al chametz dam zivchi".
"Rabbi Yehudah omer: af al hatamid" - in his view the very same prohibition applies also to the slaughtering of the afternoon tamid on erev Pesach. The source is the wording of the verse, "zivchi": "zevach" refers to the korban Pesach, and the added possessive form "zivchi", the offering that is uniquely Mine, refers to the tamid.
The approach of Rabbi Shimon: Rabbi Shimon distinguishes between the different times and between the different intentions, and his words rest on a single principle: liability depends on the validity of the offering being slaughtered.
"HaPesach b'arba'ah asar" - the Pesach offering on the fourteenth:
"Lishmo - chayav" - he slaughtered it on erev Pesach, at its proper time, for the sake of the korban Pesach: the offering is valid, and if there was chametz in his possession or in the possession of one of the members of the group, he is liable.
"V'shelo lishmo - patur" - he slaughtered it on the fourteenth not for the sake of the Pesach but for the sake of a shelamim: the Pesach is invalid. Since there is no slaughtering here of a valid korban Pesach, there is no transgression of "Lo sishchat al chametz dam zivchi", for the prohibition was stated specifically regarding the slaughtering of a valid Pesach offering.
"Ush'ar kol hazevachim, bein lishman bein shelo lishman - patur" - the other offerings slaughtered on erev Pesach, whether he slaughtered them for their own purpose (a shelamim for the sake of a shelamim) or for the sake of a different offering (a shelamim for the sake of an olah), carry no liability. Rabbi Shimon derived from the exposition of the verse that at a time when one is liable for slaughtering the Pesach because of chametz, one is not liable for the other offerings.
"Uvamo'ed" - and during the festival:
"Lishmo - patur" - one who slaughters the Pesach during the days of the festival for its own sake, after its time has passed, is exempt, even if he had chametz in his possession. Since the time of the Pesach has passed, this is not a valid korban Pesach.
The Gemara establishes this ruling in a case where the owner of the offering was tamei from contact with a corpse and was unable to bring his Pesach at its proper time, and he is destined to bring it on Pesach Sheni a month later, so that the status of a korban Pesach still rests upon it; and even so, once it was slaughtered not at its proper time it is not a valid offering, and one who slaughters it is exempt. But if he were not tamei, any Pesach slaughtered after its time, which will never again serve as a korban Pesach, has the status of a shelamim, and one who slaughters a shelamim for its own sake during the festival is liable, as will be explained. We therefore had to establish the case specifically as one who is still destined to bring a valid Pesach offering.
"V'shelo lishmo - chayav" - if he slaughtered the Pesach during the festival not for its own sake, say for the sake of a shelamim, its status is that of a shelamim and the offering is valid, and therefore he is liable.
"Ush'ar kol hazevachim, bein lishman bein shelo lishman - chayavin" - the other offerings slaughtered during the festival are valid whether slaughtered for their own sake or not for their own sake, and therefore if he had chametz in his possession he is liable on account of "Lo sishchat al chametz dam zivchi". And so it is derived from the verse: at a time when one is not liable for slaughtering the Pesach, one is liable for the other offerings.
"Chutz min hachatas sheshchatah shelo lishmah" - a chatas that was slaughtered not for its own sake is invalid, and since it is an invalid offering, even during the festival and even when he has chametz in his possession he is exempt. In this the chatas differs from the other offerings, which remain valid even when slaughtered not for their own sake, and therefore one who slaughters them during the festival while he has chametz in his possession is liable.