Because annoying, putting it out of one's mind (10)
I believe the answer is:
forgetting
'putting it out of one's mind' is the definition.
I can't tell whether this definition defines the answer.
'because annoying' is the wordplay.
'because' becomes 'for' (I've seen this in another clue).
'annoying' becomes 'getting' (I can't explain this - if you can you should believe this answer much more).
'for'+'getting'='FORGETTING'
Can you help me to learn more?
(Another definition for forgetting that I've seen is " Leaving (something) behind".)