Cut a favourite piece from a paper (7)

I believe the answer is:

snippet

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

'piece from a paper' is the definition.
'snippet' can be an answer for 'piece' (snippet is a kind of piece). I'm unsure of the 'from a paper' bit.

'cut a favourite' is the wordplay.
'cut' becomes 'snip' (snip is a kind of cut).
'a favourite' becomes 'pet' (synonyms).
'snip'+'pet'='SNIPPET'

Can you help me to learn more?

(Other definitions for snippet that I've seen before include "Small extract" , "A cutting" , "piece from the paper" , "Bit (of info?)" , "Fair --, knitwear style" .)

I've seen this clue in The Globe and Mail.

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