The most common and most likely answer to this crossword clue is the 10 letter word FRUITARIAN
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Buddy explains!
The straight part
We know that "Following a limited diet" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case following a limited diet = fruitarian.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 FRUITARIAN mean?
FRUITARIAN noun- A variant of vegetarian who intends to be limited to eating only such parts of plants whose consumption does not kill the plant (such as fruits, vegetables that can be compared to fruit, nuts and grain, but not for example tubers). The purest fruitarians do not want to destroy even the seeds.