Cryptic crossword clue
Having tossed fag out, I’m in process of cleaning up 10

The most common and most likely answer to this crossword clue is the 10 letter word FUMIGATION

I've seen this crossword clue in The Sunday Telegraph
F
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M
I
G
A
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N

Buddy explains!

The straight part
We know that "process of cleaning up" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case process of cleaning up = fumigation.
The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.
This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.

What does FUMIGATION mean?

FUMIGATION noun
  1. The act of fumigating, or applying smoke or vapor, as for disinfection.
  2. Vapor raised in the process of fumigating.

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