To fully address your question, I would need to know the context of the note which you quote. However, the Gemara writes that one must cut the veins in the case of consecrated animals, since the object of the Shechitah is to obtain the blood (for the sake of the service of Zerikah, sprinkling the blood, which is the process of the Korban that attains atonement for the owner).

D. Zupnik