What is the best way to get from St moritz Switzerland to Vienna Austria outside of flying as there doesnt seem to be a rail schedule that connects to Vienna?

Are you sure there isn't a rail connection? I am pretty sure there is since Vienna is one of the primary cities in Europe. Try again looking for one because the rail system is very good in Europe. You may have to go from St. Moriz to a German stop and from there Vienna. Try looking at it that way. If that is truly the case the bus system is very good too.