He graduated from the Theological Seminary in Kaunas in 1895 and went on to receive a master's degree from the Roman Catholic Theological Seminary in St. Petersburg in 1899. Šaulys was then appointed curate at Saint Peter and Saint Paul parish in Panevėžys. He was involved in a number of political, charitable, and educational institutions; in 1917 he participated in the Vilnius Conference, and signed the Act of Independence of Lithuania in 1918.
Šaulys specialized in canon law and moral theology, serving as a professor in these subjects at the Kaunas Theological Seminary from 1922 to 1941. He published a number of articles on religious jurisprudence, including those sections of the Provisional Constitution that dealt with religion.