Cruelly slash site bid and deprive of official support (12)

I believe the answer is:

disestablish

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'deprive of official support' is the definition.
I can't judge whether this defines the answer.

'cruelly slash site bid' is the wordplay.
'cruelly' indicates anagramming the letters (I've seen this in other clues).
'slash'+'site'+'bid'='slashsitebid'
'slashsitebid' with letters rearranged gives 'DISESTABLISH'.

'and' acts as a link.

Can you help me to learn more?

(Other definitions for disestablish that I've seen before include "Make unofficial" , "keep church separate" .)

I've seen this clue in The Times.

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