The Great Schism was a result of a power battle between the Patriarchs of the church, being based in Rome, Constantinople, Antioch, Jerusalem and Alexandria. They were supposed to be "first among equals", however Jerusalem and Alexandria were under Muslim control, and Antioch was the front line between Byzantines and Turks, so Constantinople and Rome were really the only 2 with power. Rome claimed primacy on some matters (such as appending "and the Son" to "We believe in the Holy Spirit, which proceeds from the Father." in the Nicene Creed ), and a few other issues caused them to break part. I don't think there was much blood until the sack of Constantinople during the 4th Crusade in 1204.