Doesn't eat the green stuff (6)

I believe the answer is:

leaves

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'doesn't eat' is the definition.
(I've seen this before)

I don't understand how the remainder of the clue works.

(Other definitions for leaves that I've seen before include "''All the ... are brown'' (California Dreamin')" , "Foliage - goes away" , "some tea, perhaps" , "exits" , "''... of Grass'' (Walt Whitman)" .)

I've seen this clue in The Globe and Mail.

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