Putting thoughts out of your mind and completely clearing your mind appear to be distinct processes, and they both require active work. Being able to ignore is closely related to directing attention, so poor performance at putting information out of mind results in easy distractibility and inattention.
Studies looking at the ease or difficulty of 'ignore' seem to suggest that although general tendency may be inherited, it can be strengthened by practice. In behavior tests of school age children, training in being able to resist distraction also generalized to more delayed self-gratification behaviors. The abstract of the article which discusses this in more detail is linked below.
The authors also note that when teaching children skills to reduce distraction, the challenges should be introduced gradually:
"The level of difficulty of the tasks by which the child is challenged should be adjusted so that the child can develop an expectancy that success is possible. Once that momentum has been achieved, the difficulty of the situation can gradually be ratcheted up."
The take-home message: "Like a muscle, it appears to be fatigued in the short run and strengthened in the long run by exercise."
Suppressing vs Clearing Thoughts
Self-Control: Theory and Research.