By oppression and judgment he was taken away; and as for his generation, who considered that he was cut off out of the land of the living, stricken for the transgression of my people? (Isaiah 53:8 ESV)
Then Jesus, calling out with a loud voice, said, “Father, into your hands I commit my spirit!” And having said this he breathed his last. (Luke 23:46 ESV)
Isaiah prophesied that Jesus would die. His Old Testament writings are sometimes called the fifth gospel because they are full of so much prophetic writing about Jesus. Jesus fulfilled all of Isaiah's prophecies. Jesus did die on the cross.
Some people today do not believe that Jesus actually died on the cross. They believe he was crucified, and that he just passed out or something. That's just simply not the case. Jesus died. He breathed a final breath. His spirit left his mortal body.
Jesus final breath marked a turning point in the history of humanity. His sacrifice was complete. There was still some stuff left for him to do. But the dying part was over. It had happened. It was complete. And sin was paid for.