While performing shechita, a shoichet also cuts veins and arteries next to the windpipe and foodpipe. These are not required to be cut for the Shechitah. How does this not make the animal a treifa?
Avrohom Tzvi Elias, Haifa, Eretz Isroel
Rashi (20b DH v'Chi) tells us that even though every Shechitah makes an animal a Tereifah before the Shechitah is completed (since the esophagus is punctured during the Shechitah), nevertheless this does not prohibit the animal. The reason for this is that the puncturing of the esophagus is done as *part* of the Shechitah, so it does not make the animal a Tereifah. If a person pauses during the Shechitah, after puncturing the esophagus, and continues the Shechitah at a later time, the animal will indeed be a Tereifah (Chulin 32a).
However, your question is that there is no Mitzvah to cut the arteries of an animal during Shechitah, and as such cutting these arteries should not be considered part of the Shechitah. If so, if one cuts the arteries during the Shechitah (before the Shechitah is completed), the animal should be a Tereifah.
Cutting the arteries does not make the animal a Tereifah (see YD 23:6). Although it is prohibited to eat a Mesukenes (dying) animal that was slaughtered, apparently there is not enough time between the cutting of the arteries and the Shechitah to make it a Mesukenes.
M. Kornfeld