How many people were killed by the Sanhedrin around the time of Paul? In the Bible, the Sanhedrin condemned:


Jesus
James the Just
Stephen


The death penalty was supposed to be rare, as Mishnah Makkot 1:10 states:


  A Sanhedrin that puts a man to death once in seven years is called a murderous one. R. Eleazar ben Azariah says 'Or even once in 70 years.' R. Tarfon and R. Akiva said, 'If we had been in the Sanhedrin no death sentence would ever have been passed'; Rabban Simeon b. Gamaliel said: 'If so, they would have multiplied murderers in Israel.'


Yet they killed at least 3 in about a 40 year period, and those are only the prominent ones.

How many people total did they kill, and why did they deviate from the accepted wisdom about capital punishment?

This is not to promote antisemitism. I'm simply interested in the historical facts.
How many they killed is not easy to know in absence of any historical records. They must have killed many and they did conspire to kill these three prominent ones and few more.The Sanhedrin did not have the power under Roman authority to put someone to death (Jn 18:31). This power was supposedly revoked in 30 A.D. But that did not keep them from hatching conspiracies in these meetings to get their opponets killed and they were only short of passing a formal death sentence.  

Plotted to kill Jesus through Romans:   

In absence of this power, Sanhedrin plotted to have Him murdered (Jn 11:47-53), paid Judas Iscariot 30 pieces of silver to betray Jesus (Mt 26:14-16)(Mk 14:10-11)(Lk 22:1-6), had Him arrested and tried Him using false witnesses to accuse Him (Mt 26:47-66)(Mk 14:43-65)(Lk 22:47-53)(Jn 18:1-27), then pressured Pontus Pilate into having Him crucified (Mt 27:1-26)(Mk 15:1-15)(Lk 23:1-25)(Jn 18:28-19:16).  

Also  this court was to meet every day during daytime hours and was not to meet on the Sabbath or holy days,but broke this rule to condemn Jesus.  

They plotted to kill James the just and Stephan:  

According to the Jewish historian Josephus, in 62 A.D. the High Priest named Ananus assembled a Sanhedrin who condemned James, the Lord's brother, "on the charge of breaking the law" and had him stoned to death.    

They also got Stephan killed by infuriating a mob:The Sanhedrin listened to the charges brought against Stephen (Acts 6:8-7:1) and then allowed the murder of Stephen by stoning (Acts 7:54-60).   

Also in addition to these three:  

The Sanhedrin also ordered Peter and John not to proclaim the name of Jesus (Acts 4:1-22), and when they would not stop, they had them beaten (Acts 5:17-42).  

Paul was brought before the Sanhedrin and spoke to them (Acts 22:30-23:6), and afterwards they conspired to murder him (Acts 23:12-22).  

Why this historical nuance?  

Truly the Stakes were  very high and if we agree with your view that "Sanhedrin that condemn one man to death in 75 years is bloody" then killing of these prominent three, can be only described as a knee jerk action in a do or die situation to arrest a budding movement that was to change the face of this world. Jewish authorities had rightly judged this movement as not any ordinary one.  Jews had already lost their political clout and now they were in the process of  losing their religious hold on general Jewish public. This echoed in Bible:  

John 11:47–48  


  Then gathered the chief priests and the Pharisees a council, and said, What do we? for this man doeth many miracles. If we let him thus alone, all men will believe on him: and the Romans shall come and take away both our place and nation.