Who ordered Saint Stephen to death? I have learnt that some of the Jews linked to the early Jewish council stoned St. Stephen to death and Paul as a witness. But I have a bit of confusion that who ordered the decree of Stephan's death.
Who ordered Saint Stephen to death?

No individual person ordered St. Stephen to be stoned to death. If in fact someone had ordered Stephen’s execution, I believe St. Luke would have named that individual in the Book of Acts. 


  At this they covered their ears and, yelling at the top of their voices, they all rushed at him. - Acts 7:57


Moreover, the Jews themselves made a point of making known the Roman authority in regards to executing someone to Pilate himself when they wanted Jesus put to death!


  31 Pilate said, “Take him yourselves and judge him by your own law.”
  
  “But we have no right to execute anyone,” they objected. - John 18:31


General consensus has it that the crowd spontaneously has him stoned. St. Stephen’s words in themselves infuriated the the Jews listening to his words. In today way of thinking, I would suspect that the modern phrase that it was due something like to a spontaneous local public uprising in the affair of St. Stephen’s stoning.

Simply put St. Stephen’s words infuriated the Jews standing before him.

It is equally possible that some members of the Jewish Sanhedrin or even the high priest that year, could have influenced the decision made by the crowd, for some of them were present!


  The stoning of Stephen
  
  Thus castigated, the account is that the crowd could contain their anger no longer. However, Stephen looked up and cried, "Look! I see heaven open and the Son of Man standing on the right hand of God!" He said that the recently executed Jesus was standing by the side of God.[9][Acts 7:54] The people from the crowd, who threw the first stones laid their coats down so as to be able to do this, at the feet of a "young man named Saul" (later known as Paul the Apostle). Stephen prayed that the Lord would receive his spirit and his killers be forgiven, sank to his knees, and "fell asleep".[Acts 7:58–60] Saul "approved of their killing him."[Acts 8:1] In the aftermath of Stephen's death, the remaining disciples fled to distant lands, many to Antioch.[Acts 11:19–20] - Saint Stephen


Knowing that the Jewish nation was under Roman occupation; they did not have the right to put any man to death. Thus, it only makes sense that his death was due to a popular uprising, thus keeping both the High Priest and the Jewish Sanhedrin away from being considered as ignoring the Roman authority’s powers.

Seeing that the high priests could easily be deposed by Roman authority, it would be highly unlikely that Caiaphas would have been willing to to implicated in Stephen’s death in 34 AD. 

In any case he was eventually deposed in 36/37 AD.


  Joseph Caiaphas
  
  Caiaphas was the son-in-law of Annas, by marriage to his daughter. He was appointed by the Roman governor Valerius Gratus in AD 18 (Jos Ant 18:2:2), and ruled as high priest for eighteen years. This was the longest reign of any high priest in New Testament times. He remained high priest under Pontius Pilate, and was finally deposed in AD 36 by Vitellius, the governor of Syria. He was replaced by Jonathan, another son of Annas (Jos Ant 18:4:3). Pontius Pilate was removed from office a few months before Caiaphas, after killing large numbers of Samaritans (Jos Ant 18:4:2). Caiaphas was replaced by Jonathan, another son of Annas