John 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. …

Homily on Acts 39 ↗

Theophylact of Ohrid

"Having shaken out his garments, he said to them," in order to frighten them not by word only, but also by deed. "Your blood be upon your own heads." An obscure saying. I think Paul is saying: "Everyone who falls away from Christ, Who is life, is seen as killing himself, since he passes from life to death and through the murder inflicted upon himself sheds in a certain way his own blood." Or he is saying the following: "For the fact that through unbelief you are killing yourselves, you yourselves will answer before the judgment, …

Commentary on Acts ↗

Oecumenius

"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. …

Commentary on Acts ↗