Griggs's careers in both the church and social welfare sphere were active and itinerant. In Houston, he helped establish the National Civil and Religious Institute. In 1914, he founded the National Public Welfare League. From 1925 to 1926, he served as president of the American Baptist Theological Seminary, which his father helped found. His longest tenure—19 years as pastor of Tabernacle Baptist Church in Memphis—saw him act on his belief in the social mission of churches, providing the only swimming pool and gymnasium then available to African Americans in the city.