The most common and most likely answer to this crossword clue is the 13 letter word FRAGMENTATION
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More clues leading to the result FRAGMENTATION
Buddy explains!

The straight part
We know that "Breaking up" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case breaking up = fragmentation.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 FRAGMENTATION mean?
FRAGMENTATION noun- The act of fragmenting or something fragmented; disintegration.
- The process by which fragments of an exploding bomb scatter.
- The breaking up and dispersal of a file into non-contiguous areas of a disk.
- The breaking up of a data packet when larger than the transmission unit of a network.