HELP!! 1930's home has SEVERELY clogged shower drain?

Call a pro. They can send a camera down to see what's going on down there. Don't cut the pipe. That will probably only bring you more problems without solving the original one. I'm with some of the other posters here. In a home that age, you probably have clay and/or cast iron pipes that have either settled so they don't drain like they should, or they are just plain past their useful life. I've had 2 homes that vintage and both suffered from drainage problems. One had clay pipes that had settled and broken, and with the other we never did figure out what was wrong(the plumbers suspected a fault in the city's line but the city didn't agree) and ended up installing a new line to the street and a backflow preventer.