The Torah teaches that it is forbidden to kill an animal and its son on one day (oto ve’et b’no lo tishhatu b’yom ehad – see Vayikra 22:28). This is understood by the Sages as forbidding the slaughter of a mother and its child together (some understand that it refers to the father, as well, if his identity is known).
In a case where the se’ir ha-mishtale’ah – the scapegoat – has already been chosen and an emergency situation comes up (e.g. meat is needed for someone who is deathly ill, which would allow its preparation even on Yom Kippur) for which its mother is slaughtered, would the scapegoat still be sent off to be killed, or does the rule of oto ve’et b’no lo tishhatu b’yom ehad still apply? (The Ritva points out that the question would apply even if the mother was slaughtered in a forbidden situation on Yom Kippur, but the Gemara preferred to offer a case where it would, theoretically, be permissible.)
The Gemara suggests that this is not a problem at all, since the language of the pasuk clearly states that what is forbidden is shehitah – ritual slaughter. Thus, the halakha is that if the mother animal is killed in some other fashion, it would be permissible to slaughter the child. Since the se’ir ha-mishtale’ah is to be killed by being thrown off a cliff in the desert, it would appear that the rule of oto ve’et b’no lo tishhatu b’yom ehad should not apply.
The Gemara answers: They say in the West, i.e., Eretz Yisrael, that pushing it off the cliff, which is the manner in which the scapegoat is supposed to be killed, is considered its slaughter.
In essence, the question debated on our daf is how narrowly we should define shehitah. Tosafot suggest that this Gemara is teaching us that it should be defined broadly, to mean that it was killed for its ritual purpose. In the case of the se’ir ha-mishtale’ah, that is accomplished by means other than traditional slaughter.