See you cut round tail of puppy, trimming top back on petite pet (3,6)

I believe the answer is:

toy poodle

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'pet' is the definition.
The answer and definition can be both animals as well as being singular nouns.
Perhaps there's a link between them I don't understand?

I can't explain the rest of the clue.

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(Another definition for toy poodle that I've seen is " Miniature curly-haired dog".)

I've seen this clue in the Sydney Morning Herald.

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