If you remember correctly, the movie ends just before the vietnam war.
So we don't get to see the blood bath, or Saya's insanity unfold. But we know the series picks up after the events in the film because characters like David and Karl keep on saying " 30 years ago blah blah blah Saya was crazy."
By the way David, Lewis and Saya were the only charactersfrom the series featured in the film.
While viewing the film isn't like a must or anything, I think seeing it would help you understand how miserable Saya was before her new life and why she may have gone insane.
Here is a character bio I found on the film website:
Saya, the film's mysterious, brooding protagonist, is played by the vivacious Youki Kodoh, who recently made her Hollywood debut in the feature film Snow Falling on Cedars.
A loner expelled from human society as well as the domain of beasts,paying heed to no one, beholden to no one - this beautiful nocturnal creature simply roams the darkness, bringing about a cruel destiny to all those who cross her path. Only undying legends will forever capture the tale of this accursed creature.
Some hints about Saya/Diva's? orgins taken from the film website but explained in more detail in the novel Blood the Last Vampire Night of the Beast: