Why does it need to move? Too big? Not good enough conditions?

Your best bet would probably be to wait for fall, and then dig a really big, really deep hole to take it out. Clematis roots run deep and wide, so this is really key, especially since your plant is 3y/o and is "mature". You may be able to move it now (I'm not familiar with your zone) using the same method. Make sure you have prepped the location you are moving it too before you start digging the plant up.