Cut piece, dry inside (6)
I believe the answer is:
bisect
'cut' is the definition.
(bisecting is a kind of cutting)
'piece dry inside' is the wordplay.
'piece' becomes 'bit' (bit is a kind of piece**).
'dry' becomes 'sec' ('sec' can be similar in meaning to 'dry').
'inside' is an insertion indicator.
'bit' placed around 'sec' is 'BISECT'.
(Other definitions for bisect that I've seen before include "Cut equally in two" , "Halve (angle)" , "Divide into two equal parts" , "Cut twenty [IN TWO]" , "create schism?" .)