I have heard that Orthodox Christians are forbidden from eating food containing blood (black pudding, blood sausage, etc). Is this true? What is the purpose of this prohibition and how can it be justified in light of Matthew 15:11?
"It is not what goes into the mouth of a man that makes him unclean and defiled, but what comes out of the mouth."
As you understand it is not possible to completely drain the meat from the animal's blood. So whenever we eat meat, we inevitably eat some blood left in the meat in small quantities. So, since we eat blood whenever we eat meat, the ban on the consumption of blood does not mean that the blood is unclean food.
Explanations from the "Rudder" (by St. Nicodemus of the Holy Mountain):
Theodoret of Cyrus says: you should not eat blood, wherefore it is the soul of the animal
St Chrysostom says: you should not eat blood, because it was devoted only to God. Also because God wanted to prevent people not to spill human blood, for it commands neither to eat animal blood so as not thus litle-by-litle become accustomed to homicide.
Clement of Alexandria says: you should not eat blood, because your flesh too is developed and built by blood