Why vampires do not have teeth?

No, if by 'Twilight' you mean the book series by Stephenie Meyer.

The Twilight vampires are different from conventional vampires in several ways, their lack of fangs one of them.

They have teeth like regular humans, but they are razor sharp and can cut through most substances; notably vampire skin, which is described as being hard as granite.

Their venom is believed to be 'coating' on their teeth, transferring to the body of the victim through the bite. In Midnight Sun, Edward describes being near a human while hungry causing an 'excess flow of venom' to his mouth. From this it can be compared to the human sensation of 'drooling at the mouth' when hungry or a particularly appetising food is present.