Imagine it is freshly amputated and is still alive,
Why should I imagine it when that's not reality?
or that we amputate it and hook it up to an artificial circulatory system, or indeed my circulatory system but at a distance so nothing else is connected (curious if you think the pain chance changes in that situation).
Where it would be no more "alive" than Henrietta Lacks' eternal cell line. If you have to keep it from decomposing by artificial means, it's not alive like a plant is alive. This should be obvious to you.