Odd cut of meat with last slice removed (3)

I believe the answer is:
rum
'odd' is the definition.
(rum can mean strange or dubious)
I don't understand how the remainder of the clue works.
Can you help me to learn more?
(Other definitions for rum that I've seen before include "Odd like drink distilled from molasses" , "Spirit (in the punch?)" , "Odd sort of drink" , "Strange drink from molasses" , "Sugar-cane product" .)
