Cocktail one’s knocked back: short to follow (3,3)

I believe the answer is:

mai tai

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'cocktail' is the definition.
(I've seen this before)

'one's knocked back short to follow' is the wordplay.
'one's' becomes 'iam' (I can't explain this - if you can you should believe this answer much more).
'knocked back' shows that the letters should be reversed in order.
'short' means to remove the last letter.
'to follow' becomes 'tail' (both can mean to chase or pursue).
'iam' reversed gives 'mai'.
'tail' with its final letter removed is 'tai'.
'mai'+'tai'='MAI-TAI'

Can you help me to learn more?

(Other definitions for mai tai that I've seen before include "drink?" , "Cocktail" .)

I've seen this clue in The Times.

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