Since, they are partly humans possessing a human body, they do have blood. But it's a little different from the kind of blood human body has. A vampire's blood isn't good for another vampire. Also human blood is nutritious and the only source of food for vampires.
The most profound differences between humans and vampires are found in the circulatory system. These differences enable vampires to survive massive trauma that would kill a human being.
Blood: vampire blood is called ichor (pr. ik-er). Modifications to hemoglobin in the blood cells makes vampire blood appear black.
the Heart: vampire blood is pumped via the contraction of skeletal muscle rather than the heart, which eventually atrophies from disuse.