We didn’t have much luck finding a quick way to get from Seoraksan National Park to Andong. Although it looked like it would have been possible to take a train, or a combination of buses going through Donghae, or Chuncheon, we were not confident this would work.
We ended up giving up and taking a local bus from Seorak back to Donghae, then taking a bus all the way back to Seoul, then another bus on to Andong. We could do all this without changing bus stations in either Donghae or Seoul, and there’s lots of buses along both the Donghae to Seoul and Seoul to Andong routes. It took us about 7 hours. It might have been only 5 hours if we spoke Korean and had been able to talk to people and been confident that a more direct route would have worked.