Starter of tree tufts rejected; detox's not half restricting Everyman in regime (6,4)

I believe the answer is:

bloody mary

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'starter' is the definition.
(I know that Bloody Mary is a IBA official cocktail)

I can't explain the rest of the clue.

Can you help me to learn more?

(Other definitions for bloody mary that I've seen before include "Tomato juice and vodka" , "Nickname of Henry VIII's first daughter" , "Queen regarded unfavourably" , "The Red Queen" , "it could be an eye-opener" .)

I've seen this clue in The Everyman puzzle in The Observer.

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