The cord cutting ritual is very good for breaking ties with another person in the past that you still feel connected to energetically. However, if there is something else from the past that you are still connected to in this way I would think that it would be also effective. But it is typically some "thing" or some "one" in the physical world that this ritual is used for.
With that being said, if it is a thought form that is related to the past that is still connected to you energetically in the present I would think that this ritual could also be useful. What you would need to do is use an image of something physical as a symbolic representation of this thought form in place of it.
Although I live in Mexico currently, I lived in northern New Mexico for nearly twenty years and am very connected to the land in that area. So for myself I visualize a specific place there – the Rio Grande Gorge. It is this beautiful place with a very deep crevasse that has been carved by the Rio Grande river. This is where I go in my mind's eye when I have performed this on myself. You can meditate on this image for a while and use it in this ritual, or you might have your own imagery that will work equally as well.
What I have done (and recommended to clients of mine when I lived in the region) is that in my mind's eye I have "met" the person I am wishing to break ties with in the middle of the bridge. We are connected to each other from the navel by a long, thick cord. We meet on the bridge, face to face, and say nothing. We simply take a moment to look into the eyes of one another. Then each of us turns our back and we slowly walk to opposite sides of the bridge. When we make it to the edge, the bridge disappears and we find ourselves standing on opposite sides of the massively deep canyon that cannot be crossed. The cord is still connecting us.
I stand on my side of the canyon and quietly acknowledge to myself what the connection to this person has done for me. What lessons have I learned from this relationship and how have I grown? What were the gifts that I have received? I take a moment of gratitude for this and for the person. Then I say to myself that that it is now time to sever the connection. At this point I will take any object for cutting – scissors, axe, sword, chainsaw – whatever it takes – and I cut the cord that is connecting us together. I may need to saw at it and really work hard to sever the ties, or perhaps it is as simple as a single snip. When it happens, however it happens, I watch the cord drop from my navel, slip away from my side of the gorge and fall into the depth of it. I see that the connection is severed and it cannot be reinvigorated.
It is as simple as this. It may be helpful to enter this place through meditation, candles, prayer, incense or anything else that will help take you to this space. It is also good to utilize any emotions that come up for you during the ritual. Take in the emotions that come up and allow yourself to feel them fully. Take in the emotions, experience them, process them and then when the ceremony is complete you can move beyond them.