The reason they wanted to sentence Jesus to death was because they were convinced that Jesus had committed the sins of temple desecration and blasphemy.

When the high priest said to Jesus, "I charge you in the name of the living God: Tell us if you are the Christ, the Son of God," Jesus replied, "Yes, it is as you say. But I say to you all: In the future you will see the Son of Man sitting at the right hand of the Mighty One and coming on the clouds of heaven."  Then the high priest tore his clothes and said, "He has blasphemed!  Why do we need any more witnesses?  Look, now you have heard the blasphemy.  What do you think?"  "He deserves death," they all answered (Matthew 26:63-66, Modern Bible Translation).  This was because, from the perspective of the high priest and the Jews, they believed that "the Lord our God, the Lord is one" (Deuteronomy 6:4, Modern Bible Translation).  So when Jesus said, "I and the Father are one," the Jews picked up stones to stone Him. (John 10:30-31, Modern Bible Translation).  Ultimately, the reason the chief priests and the Jewish Sanhedrin wanted to put Jesus to death (Matthew 26:59, Contemporary English Version; Matthew 26:66) was because they were convinced that Jesus had committed the sin of desecrating the temple (v. 61) and blasphemy (vv. 63-65).