I have an old house with cast iron plumbing and vent stack. The weight of the cast iron is taking its toll on the plumbing. I want to replace the heavy cast iron stack with pvc. How can I remove the old cast iron stack without tearing out a wall to get to it?

Well something's going to be tore up. You're going to hafta tear uothe floor and remove every single branch down to the stack,(including the hubs) Then, if you're lucky, you could take a set of ratchet cutters in the basement and "nibble" that sucker down in short lengths.
So much for the easy part!
The fun's going to began when you start to replace with PVC and tie the branches back to the stack.
Good luck, Tom