Waste last of the burger (big one!) I was consuming (8)
I believe the answer is:
emaciate
'waste' is the definition.
('emaciate' can be a synonym of 'waste')
'last of the burger big one i was consuming' is the wordplay.
'last of' suggests the final letters.
'burger big one' becomes 'mac' (Big Mac).
'was consuming' becomes 'ate'.
The last letter of 'the' is 'e'.
'e'+'mac'+'i'+'ate'='EMACIATE'
(Other definitions for emaciate that I've seen before include "Make extremely thin" , "Waste away" , "get very thin" .)