The most common and most likely answer to this crossword clue is the 6 letter word HUMBLE
I've seen this crossword clue in Independent
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More clues leading to the result HUMBLE
Buddy explains!

The straight part
We know that "Of modest dimensions/cut down to size" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case of modest dimensions/cut down to size = humble.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 HUMBLE mean?
HUMBLE noun- (Baltimore) An arrest based on weak evidence intended to demean or punish the subject.
- To defeat or reduce the power, independence, or pride of
- To make humble or lowly; to make less proud or arrogant; to make meek and submissive.
- Not pretentious or magnificent; unpretending; unassuming.
- Having a low opinion of oneself; not proud, arrogant, or assuming; modest.
- Near the ground.
- A stag that has failed to grow antlers; a cow that has not developed horns.
- Especially in hummel corn: grain that lacks awns (beards or bristles), or has had its awns removed (barley, oats, etc.).
- Of an animal: to remove the horns; to poll.
- To separate (barley, oats, etc.) from the awns.