More generally, under modern penal theory, almost all criminal statues have two components, mens rea and actus reus. Actus reus is the prohibited act, what most people think of as the crime (“screwing the pooch” being the example here).
However, in addition to a prohibited act, the actor must have the mens rea, the culpable mental state, identified in the statute, in this case “knowingly”. Other commonly used types of mens rea in criminal statutes are “intentionally”, “recklessly”, and “negligently”. A limited number of crimes are strict liability crimes, where the act is criminal regardless of the mens rea of the actor, such as statutory rape, where if you have sex with someone underage it is criminal regardless of your knowledge or understanding of the facts.
Another reason that “knowingly” is important in this statute is that it does not only cover the act of beastiality, but also aiding or permitting someone to commit the act. If you innocently but foolishly let Uncle Creepy dogsit your rottweiler and you walk in to find a rutting rottie, you have aided or permitted the act, but not done so knowlingly.