The most common and most likely answer to this crossword clue is the 10 letter word BIODEGRADE
I've seen this crossword clue in The Times
B
I
O
D
E
G
R
A
D
E
More clues leading to the result BIODEGRADE
Buddy explains!

The straight part
We know that "break up, naturally" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case break up, naturally = biodegrade.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 BIODEGRADE mean?
BIODEGRADE verb- To decompose as a result of biological action, especially by microorganisms