When Jesus died did he die a Jew?

Yes, The Scepter promise was given to Israel's 4th son Judah(Genesis 49:10). It involved the Salvation of all Mankind by Jesus Christ, the Son of God and the Son of Man. Jesus was born into the line of King David and was a Jew. He lived and died as a Jew.

He preached 1st to the Jews as prophecized. He sent all of His Apostles to the scattered House of Israel which included the Jews abroad except Paul who had a special mission to the Gentiles but also preached to the Jews & Gentiles in Synagogues. Remember, the House of Israel had 12 tribes with Joseph's 2 sons being adopted by Israel and getting a double share of blessing with many interpreting the Genesis blessings to Joseph's sons with Ephraim as the British Commonwealth Nations and Manasseh as the United States. Are the Lost Tribes of Israel really still lost?

Gentiles can now be grafted into the Tree of Life and must repent and be baptized to receive Gods Holy Spirit (aka Spirit of Christ) and become Spiritual Israelites as Paul explains in Hebrews 9 & 10.