Goaslind was born in Salt Lake City, Utah, to Jack, Sr. and Anita Jane Jack. As a young man, Goaslind served as a missionary for the LDS Church in the Western Canadian Mission. Goaslind had been an avid skier since childhood and by choosing to serve a mission, he passed up a chance to train for the Olympics with the United States Ski Team. After his mission, he graduated from the University of Utah and became a vice president with Affiliated Metals, Inc. Goaslind married Gwen Bradford and they had six children.
Goaslind served in the LDS Church as a bishop, stake president and a regional representative. In 1972, he was called as second counselor to Young Men general president Robert L. Backman. When the church's presiding bishopric assumed supervision of the Young Men program in 1974, Goaslind was released and served as president of the church's Arizona Tempe Mission.
In 1978, Goaslind became a general authority and member of the First Quorum of the Seventy. From 1979 to 1981, he was second counselor to Hugh W. Pinnock in the general presidency of the church's Sunday School. In 1985, he became a member of the seven-man Presidency of the Seventy, a position he held until 1987, when he became president of the church's British Isles–Africa Area. During this time, he oversaw placing Emmanuel A. Kissi in charge of the church's affairs in Ghana during "the freeze", when the government of Ghana forbade all meetings of the church.
In 1990, Goaslind succeeded Vaughn J. Featherstone as general president of the Young Men. During his eight-year tenure, Goaslind had seven different men as counselors, more than any other Young Men president in history. In 1995, Goaslind was again added to the Presidency of the Seventy. He was released from the Presidency of the Seventy and from the presidency of the Young Men in 1998, when he was granted general authority emeritus status. In the leadership of the Young Men, he was succeeded by Robert K. Dellenbach, his first counselor. From 2000 to 2003, Goaslind was president of the church's Manti Utah Temple.
In 2007, he was inducted into the Order of Saint Michael of the Wing by the Royal House of Braganza, which ruled Portugal until 1910. Goaslind was selected for his humanitarian efforts in the former Portuguese colony of São Tomé and Príncipe while he was the president of the British Isles–Africa Area.