Q. Why did the soldiers who crucified Jesus go beyond Pilate’s order?
I have to admit that I’m not entirely sure what you’re asking here.
Perhaps you are noting that Pilate declared Jesus innocent and said he would release him, and so you are wondering why the soldiers crucified Jesus anyway. Pilate said to the people who were accusing Jesus, “You brought me this man as one who was inciting the people to rebellion. I have examined him in your presence and have found no basis for your charges against him. … He has done nothing to deserve death. Therefore, I will punish him and then release him.” So when we read this, we may be surprised to discover that the soldiers put Jesus to death anyway.
However, before the soldiers took Jesus away to execute him, Pilate actually changed his mind, at the urging of the crowd. The account of Jesus’ trial continues and it says: “But with loud shouts they insistently demanded that he be crucified, and their shouts prevailed. So Pilate decided to grant their demand.” So the soldiers actually did not go beyond Pilate’s order to punish Jesus when they crucified him. Pilate changed his order and told them to crucify him.
Or perhaps you are asking why the soldiers, in addition to actually executing Jesus, mocked him and insulted him and perhaps taunted him by offering him something to drink in his great thirst but then not giving it to him. These things, unfortunately, were actually a regular part of crucifixion, whose purpose was not just to execute a condemned person, but to humiliate them and make them suffer as much as possible. The soldiers who mocked, insulted, and taunted Jesus were doing what Roman soldiers did to every person they crucified.
What is amazing is that Jesus knew he would be treated that way, in addition to the great physical suffering of crucifixion, and yet he still said to God beforehand, “Not my will, but yours be done.” Hallelujah, what a Savior!