Cuts speech oddly in pieces (7)
I believe the answer is:
bisects
'cuts' is the definition.
(bisecting is a kind of cutting)
'speech oddly in pieces' is the wordplay.
'oddly' means one should take alternating letters.
'in' indicates putting letters inside.
'pieces' becomes 'bits' ('bit' can be a synonym of 'piece'**).
The alternate letters of 'speech' are 'sec'.
'sec' going inside 'bits' is 'BISECTS'.
(Other definitions for bisects that I've seen before include "Cuts in two" , "Divides in equal halves" , "Divides into two parts" , "Cuts in half" .)