Clematis lends itself to being readily transplanted, but only during the dormant season. This fall, after the plant is thoroughly dried and brown looking, dig it up with as large a root ball as you can muster and remove to the desired new location.
You'll find that there are three varieties of clematis, each with it's own pruning needs. But, it sounds as if the one you have is one that doesn't require much pruning since it's blooming without any assistance. Even so, prune it lightly in the dormant season to control it's shape. Be sure to transplant it to a location getting considerable sunlight and a place to climb...