Acts 18:6

"Your blood be on your own heads." These words are obscure, but I think they mean this: Whoever does not believe in Christ, who is life, seems to kill himself by passing from life to death and shedding, as it were, his own blood through his self-inflicted death. Therefore he means that when you kill yourselves through disbelief, you receive the punishment of murder, so I am innocent. Following this train of thought it may be also said that he who kills himself is punished by God as a murderer. Similarly if a person is the reason why someone kills himself, he will be guilty in the same way.

"Your blood be on your own head." This is what Paul says, casting off his garments, so that one should fear not only the word but the deed as well. Therefore, having said this more strongly, "Your blood be on your own head," he departs from them. And he means this: each of those who apostatize from Christ, who is Life, seems to slay himself, passing from life into death, in a sense pouring out his own blood by the slaughter he brings upon himself. Therefore he says, "Instead of slaying yourselves through unbelief, you promise justice for this very thing, while I am innocent." From this it is clear that the one who slays himself is punished as a murderer by God. [CHRYSOSTOM]

What then does Paul? He separates from them, and in a very awful manner: and though he does not now say, "It was need that the word should be spoken unto you," yet he darkly intimates it to them: "and when they opposed themselves, and blasphemed, he shook his raiment, and said unto them, Your blood be upon your own heads; I am clean: from henceforth I will go unto the Gentiles." For wherefore having left that house did he come to live hard by the synagogue? was it not for this? For it was not that he saw any danger here. But therefore it is that Paul having testified to them--not teaches now, but testifies--"having shaken his garments," to terrify them not by word only but by action, "said unto them, Your blood be upon your own heads": he speaks the more vehemently as having already persuaded many. "I," says he, "am clean." Then we also are accountable for the blood of those entrusted to us, if we neglect them. "From this time forth I will go to the Gentiles." So that also when he says, "Henceforth let no man trouble me," he says it to terrify. For not so much did the punishment terrify, as this stung them.