Shaw was born in Butler County in southwestern Ohio. He was a member of the non-instrumental churches of Christ, also known as the Christian Church or Disciples of Christ at this time. Perhaps his best known work is the popular gospel song "Bringing in the Sheaves (words). He also wrote "Tarry with Me" and a tune used with "We Saw Thee Not" among many other works.
Shaw was a prolific evangelist as well, known for his wit, knowledge of the Bible, and ability to generate and maintain rapport with an audience. He is thought to have baptized (immersed) some 20 thousand people.
He died in a train wreck in McKinney, Texas (just outside Dallas). He was buried in East Hill Cemetery in Rushville, Indiana. His last words: "It is a grand thing to rally people to the Cross of Christ.