No. The motto "Live Free or Die" belongs to New Hampshire (official state motto since 1945, from General John Stark's 1809 toast).
Vermont's motto is "Freedom and Unity." Adopted 1788 (Vermont Republic), retained at statehood (1791). It reflects the Green Mountain Boys' ethic and the balance of individual liberty with communal responsibility.
Both states share a fierce independence streak, but their mottos are distinct.