Complex sentence: The diving response has been shown to have an oxygen-conserving effect, both during movement and at rest, saving oxygen for the heart and the brain, lengthening the time to the onset of serious hypoxic damage.
Split into simpler sentences: The diving response has been shown to have an oxygen-conserving effect, both during movement and at rest. Oxygen is saved for the heart and the lungs, slowing the onset of serious hypoxic damage.