Irritated American's expression when they bring up crazy pet (6)

I believe the answer is:

goddam

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'irritated american's expression when they' is the definition.
The definition suggests an adverb but the answer is an adverb.

'up crazy pet' is the wordplay.
'up' shows that the letters should be reversed in order (in down clue: letters go upwards).
'crazy' becomes 'mad' (synonyms).
'pet' becomes 'dog'.
'mad'+'dog'='maddog'
'maddog' reversed gives 'GODDAM'.

'bring' is the link.

Can you help me to learn more?

(Another definition for goddam that I've seen is " Blooming".)

I've seen this clue in The Irish Times.

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