This is called the 'diving reflex' and it happens with all mammals. It happens because it happens - natural selection: Animals that slow down heart rate when diving must have an advantage of doing so.. In my head the ANS responds like this... "I am diving, therefore I cannot breathe, therefore it is best to save energy and slow down the heart rate".
Lennart: The 'why' in Physiology is always a tricky question. It may be helpful to find new ideas, but in fact we call it teleology: find a phenomenon and interpret its 'meaning'.
Why would it make sense to slow HR when diving? Well, that is not the only thing that happens and Fernando is right: the diving response is found in most, if not all mammals (and in diving birds). Any textbook will give you an overview of how the energy saving and redistribution of circulating blood takes place.
Part of your own answer already is more physiological, and relates to 'how, by which stimulus'? In humans the reflex originates from cold wetting of the face. I wonder if that would also be the case in the blue whale. Stimulation of trigeminal afferents (in the nose and periorbital area) is supposed to be involved in addition to chemoreceptor afferents.
Lennard, I'd like to point you to two nice articles in the "Encyclopedia os Marine Mammals", one related to Diving Behavior (http://www.sciencedirect.com/science/article/pii/B978012373553900078X) and another to Diving Physiology (http://www.sciencedirect.com/science/article/pii/B9780123735539000791).
As stated by the other asnwers, what happens in the blue whale, and any other marine mammal, is an hypertrophy of a common mammal reflex. Since they are extreme divers (compared to terrestrial mammals), there was a strong selection for this bevahior.
Yes bradycardia is a general mammalian response that may be more profound in aquatic mammals. I attach an exchange I had almost 30 years ago with my esteemed colleague Dr Robert Elsner on this general subject with several facets. Sam Ridgway
The stimulation of some facial regions is known to trigger the trigemino-cardiac reflex: the main stimulus is represented by the contact of the face with water in land mammals. Since the blue whale is always in water heart rate is closely linked with respiration slowing after breathing through central stimulation of the vagus.
Meuwly, C., Golanov, E., Chowdhury, T., Erne, P., & Schaller, B. (2015). Trigeminal cardiac reflex: new thinking model about the definition based on a literature review. Medicine, 94(5).