he took my sins and my sorrows

This phrase in "My Savior's Love" is when it gets personal. The death of Jesus on the cross was intentional.  It was the "atoning" sacrifice.  His death paid the penalty of all humanities transgressions. "He made them His very own".  The writer of Hebrews made this point clear.Heb. 2:17 Therefore, he had to be like his brothers and sisters in every way, so that he could become a merciful and faithful high priest in matters pertaining to God, to make atonement for the sins of the people.
How Marvelous!  How Wonderful!  Praise God!