Soundly beat American in cycling stage (5)

I believe the answer is:

paste

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

'soundly beat' is the definition.
'paste' can be an answer for 'beat' (I've seen this before). I'm not sure about the 'soundly' bit.

I don't understand the rest of the clue.

Can you help me to learn more?

(Other definitions for paste that I've seen before include "Adhesive; imitation gem" , "Hit" , "Watery adhesive" , "Stick - imitation gems" , "Sticky stuff" .)

I've seen this clue in The Independent.

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