For now I will post an excerpt from an article that I found that is related to this:
Thou shalt not kill" obviously has its exceptions. We shall first look at the warrior saints of our Church. As honest Christians they served their countries often engaging in battles that required killing of people. The Byzantine and Russian empires obviously came to be through conquering, which alot of the times requered killing. When the Russians were getting rid of the Tatar and Mongol invaders, it required killing. St. Sergius of Radonezh blessed the troops to do so. He even blessed his two great-schema monks to participate in battle as warriors. St. Andrew Peresvet laid his life and killed Mamai. He did this not because he hated him, but because he loved his people, who would have died from Mamai's hand. There is nothing ungodly in what they did. Many other saints of the Holy Rus' were warriors, yet they were glorified as saints. In general the Apostle did not forbid Christians to join the army. Thus, certain institutions were blessed by the Holy spirit to take other people's lives under certain circumstances. If the regular warriors are allowed to do so, the Kings and Czars are obviously also receive that authority, since they "are sent by him for the punishment of evildoers, and for the praise of them that do well" (1 Peter 2:14) Czar "is the minister of God to thee for good. But if thou do that which is evil, be afraid; for he beareth not the sword in vain: for he is the minister of God, a revenger to execute wrath upon him that doeth evil" (Romans 13:14). If the warriors are allowed to take lives in order to protect their people and if the kings are allowed to take the lives of their subjects for certain crimes, how do we then think that ending the lives of those who not only kill bodies but also kill souls is unjust? Heretics are then must be punished and, if needed, executed more than anyone else, since they kill innocent Christian souls.
A little later I will translate a few passages from the Enlightener for those who have not read it or can't because of the language (I don't think it has ever been translated). Here come a few small points from his book. St. Theodore of Edessa traveled to the king to ask him to execute the heretics, because they were leading many Orthodox to fall into their false teachings. St. John Chrysostom told the Orthodox Christians to use violence if needed to stop the heretics from spreading their blasphemy, so that they might be "afraid of even shadows when they hear Christians somewhere". Holy apostles Peter, Paul, and John killed blasphemers and pagans through the power of the their prayer. St. Leo the Great prayed to God that he might stop the spread of heresy, and within 40 days St. Marcian slayed as many as he could. The same saint persecuted heretics severely. Same can be said about St. Constantine and many other pious rulers. There quite a few other examples on this issue. But those I found the most convincing.