Why did Satan want Jesus to die if he knew it lead to the salvation of mankind?

The Bible does not give us the answer, but the question assumes Satan knew or believed it would lead to mankind’s salvation. Had he known that fact he would likely have acted differently. While his ultimate destruction is clearly shown in Revelation 20, the New Testament had yet to be completed at the time of the crucifixion.

He was not privy to God’s plan and possibly viewed the crucifixion as a total victory, and therefore a failure on Jesus’ part for not saving himself and proclaiming himself a king as the crowds expected. Cutting off this Messiah before he had a chance to do anything significant might have seemed like the best way to thwart mankind’s salvation. 

While the Old Testament is full of prophecies of Jesus’ suffering and the events leading up to his death, even the learned Pharisees missed the import of what Jesus was doing. For example, while Jesus was on the cross, priests and Pharisees taunted him in Matthew 27:43 by quoting Psalm 22:8.

In the same way the chief priests also, along with the scribes and elders, were mocking him and saying, “He saved others; He cannot save Himself. He is the King of Israel; let Him now come down from the cross, and we will believe in Him. HE TRUSTS IN GOD; LET GOD RESCUE Him now, IF HE DELIGHTS IN HIM; for he said, ‘I am the Son of God.'”

Matthew 27:41-43 

Not realizing its context, they themselves were fulfilling prophecy and ridiculing their own Savior. 

But I am a worm and not a man, a reproach of men and despised by the people. All who see me sneer at me; they separate with the lip, they wag the head, saying, “Commit yourself to the LORD; let Him deliver him; Let Him rescue him, because He delights in him.”  Psalm 22:6-8 

Perhaps even today, in his arrogance, Satan thinks he can somehow still thwart God’s divine plan. He may think he can degrade enough humans away from God that they would be lost to second death and unable to walk up the highway of holiness in God’s future kingdom. He might consider this a sick kind of victory, wanting to bring as many away from God as possible.

To learn more about God’s plan for mankind and how it relates to Satan listen to,

“Why Doesn’t God Just Destroy Satan?”

To learn more about the prophecies concerning Jesus’ death and his fulfillment listen to,

“When Jesus Said ‘It Is Finished.” What Did He Begin?”