Divination falls under honorific sacrifice (i.e. this is communication with a god who is giving you answers via entrails) and so the sacrificed animal is offered as a gift afterward in the form of a meal that was shared by both the deity and the supplicants. They did not eat the entrails. These were usually burned in a sacrificial fire as offerings (holocaust) or tossed into the water if an aquatic deity was involved. Eggs (the reading of which was done in a vessel of water) would afterward be scooped out and specifics. In a more secular commentary, you could say food wastage was frowned upon (as a side, food offerings left at temples and crossroads were either eaten by the priests/priestesses or animals and vagrants, which was seen as just fine).

http://www.perseus.tufts.edu/hopper/text?doc=Perseus:text:1999.04.0063:entry=sacrificium-cn

This article on "sacrificium" from The Dictionary of Greek and Roman Antiquities details the different type of animal sacrifice and also a slew of primary sources that cover greater specifics.