Tranquilizing a dinosaur is an alternative to killing it. This will drop the dinosaur where it stands with a quick-acting drug. Use of the tranquilizer adds 25% to your total points acquired during that hunt.
Usually, tranquilizing a dinosaur causes it to perform a breathing animation after the "death" animaton. The only animals in the Carnivores series with no breathing animations are Dimorphodon, Pteranodon, Archaeopteryx, and Tyrannosaurus. However, the player is still awarded extra points for the Tyrannosaurus.
Despite the fact that guns are firing tranquilizer darts, all weapons keep their regular firing sounds.
By using it you can't get a trophy (confirmed on Carnivores: Dinosaur Hunter
Although the in-game description states that the darts release a quick-acting drug, you need to fully deplete the animal's health in order to sedate it, and if you don't, the animal can roam conscious forever. The description is actually just ported over from the original Carnivores unchanged, which had mortal spots meaning a dinosaur could be downed instantly.