Not really informed advice because its based on cleaning ivy of far less valuable structures, but I cut through the main stem and then peel the ivy off later when it's hold has lessened due to the dying back.
We've got a huge ugly ivy plant growing up one end of our house. It's rooted at the base of a west-facing wall and also grows round to the north-facing wall. The walls are 19th century brick and it's a listed building so I really mustn't damage it. The walls are three storeys high.
So, any advice? Is there anything I should know? Does it matter when I do it? Is it just a matter of ripping up the ivy and popping in the new plant? There's only a tiny spot to plant the creeper and I won't be able to pull up the ivy roots because the surrounding area is concreted over.