Crossword Genius

Almighty deed, changing cats for dogs - all tailless (3,2,3)

Ross

I believe the answer is:

act of god

I'm a little stuck... Click here to teach me more about this clue!

'changing cats for dogs all tailless' is the definition.
I can't tell whether this definition defines the answer.

'almighty deed' is the wordplay.
I cannot quite see how this works, but
'almighty' could be 'god' (synonyms) and 'god' is found within the answer.
'deed' could be 'act' (an action) and 'act' is found in the answer.
The remaining letters 'of' is a valid word which might be clued in a way I don't understand.
This explanation may well be incorrect...

Can you help me to learn more?

(Other definitions for act of god that I've seen before include "Divine intervention" , "Event outside human control" , "Non-insurability clause" , "An uncontrollable natural event, say an earthquake" , "Natural catastrophe - insurance company's get-out clause?" .)

I've seen this clue in The Independent.
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