Jesus was sent to spread the Good News and to die for our sins. That was the purpose of His crucifixion. He was the Lamb who died for all mankind.
The Romans may have carried out the actuial crucifixion.. But the mob of people who were there wanted His death and the release of Barrabas after Pontius Pilate, who had the power to stop His execution, refused to do so and washed his hands of the matter, giving the power of deciding His fate to the angry mob that had gathered, the majority of whom were Jewish. Mobs are notorious for killing people regardless of the nationality of the mob.
It is unfortunate that in this case, they were Jewish since the Jewish people have had to endure the blame of killing Jesus Christ, the Son of God and have been persecuted relentlessly for that action ever since. Jesus Christ forgave them saying, "Father, forgive them for they know not what they do." For He died for their sins as well as ours.
What was Jesus' crime? He claimed to be the Son of God, the Romans said. And they didn't like His popularity with the people. One of His disciples, Judas, betrayed Him with a kiss.
It has also been asked by many why Jesus didn't just come down from the Cross and refuse to be crucified since the Son of God could've used His mighty power in that way. To come down from the Cross would've been human. And as I said before, He was sent to die for our sins which He did.