A short answer to the question of how Robert Thorn is killed is that he is shot by a policeman. So, what are the events that will lead us to his death?

In the 1976 movie The Omen, Actor Gregory Peck is cast as Ambassador Robert Thorn. He is the adopted father of Damien, the son of Satan. In this picture, Thorn is a protagonist and is also portrayed as a responsible figure. It is said that he always knew his wife Katherine (Lee Remick) was emotionally unstable, but he still wanted to marry her and was a loving and caring husband. He also really loved Damien.

With the plot of the film, it has Robert concerned for Katherine throughout the story. He does everything he is capable of doing to help her. He is also a loving father, but he ultimately learns the truth about Damien. His adoptive son is the Antichrist.

After Robert Thorn knows the truth, he is attacked by Mrs. Baylock, who is around to protect Damien. Once Thorn kills Baylock, he puts Damien in his car and drives to a nearby church. He is asked to stop by a policeman on the way, but he doesn't and the police start to chase him. He reaches the church. He gets ready to kill Damien; however, he hesitates. He says "God Help Me." Thus, as he is about to stab the child, the police arrive. The police, having no idea of Damien's origins shoot and kill Robert Thorn. Damien survives everything. Was it all done purely by chance?

More Info: en.wikipedia.org