Complex sentence: He played for the Washington Senators, who relocated in 1961 and became the Minnesota Twins; he later played for the second Washington Senators franchise, which relocated to Texas after his career, and the Cleveland Indians, all of the American League.
Split into simpler sentences: He played for the Washington Senators, which relocated in 1961 and became the Minnesota Twins. He later played for the second Washington Senators franchise (which relocated to Texas after his career) and the Cleveland Indians, all of the American League.