Thinly slice second piece of offal (6)
I believe the answer is:
sliver
'thinly slice' is the definition.
'sliver' can be an answer for 'slice' (I've seen this before). I am not sure about the 'thinly' bit.
'second piece of offal' is the wordplay.
'second piece of' becomes 's' (I am not sure about this - if you are sure you should believe this answer much more).
'offal' becomes 'liver'.
's'+'liver'='SLIVER'
Can you help me to learn more?
(Other definitions for sliver that I've seen before include "Small thin sharp piece" , "Small sharp fragment" , "Tiny bit" , "Tiny slice, splinter" , "Narrow sharp fragment" .)