Göthe had initially planned to become an architect, but went on to train as a sculptor for, among others, Johan Tobias Sergel.
After completing training at the Academy of Arts in 1803 he traveled to Italy and studied under Antonio Canova.
Returning to Sweden in 1810, he completed a monument to the murdered Axel von Fersen the Younger, but did not attract any major success.
Other works were Charles XIII of Sweden's statue in the King's Garden which was unveiled in November 1821 on the anniversary of Crown Prince Charles XIV John of Sweden adoption, and the pulpit in St. Jacob's Church in 1828.
After a stay in Saint Petersburg, where he executed a seated colossal statue of Catherine the Great, he was appointed member of the city's art academy.