In the awakened spiritual life, the key is not merely to get rid of the heart's clutter, but to live unattached to it, without identification with all that causes you to love it and want to hold onto it. You want to get to the place where you no longer feel compelled to have it around, period. This freedom is the fruit of interior prayer, watchfulness, awareness.
Continual, habitual returning to that deep union with Christ within means that you become increasingly non-attached and disidentified with the thought-clutter that once littered your inner life, though you probably could not see it at the time.