Mired in a smelly problem with egg flip - drink's first ingredient not working (6,4)
I believe the answer is:
bogged down
'mired' is the definition.
('bog down' can be a synonym of 'mire')
'a smelly problem with egg flip drink's first ingredient not working' is the wordplay.
'a smelly problem' becomes 'bo' (body odour).
'with' says to put letters next to each other.
'flip' shows that the letters should be reversed in order.
'first ingredient' says to take the initial letters.
'not working' becomes 'down'.
The initial letter of 'drink' is 'd'.
'egg' reversed gives 'gge'.
'bo'+'gge'+'d'+'down'='BOGGED DOWN'
'in' acts as a link.
(Other definitions for bogged down that I've seen before include "Encumbered with too much work" , "as a peat-cutter?" , "Overwhelmed" , "Literally or figuratively stuck in the mud" .)