Given the chop by a cross editor (4)
I believe the answer is:
axed
'given the chop' is the definition.
(I've seen this before)
'by a cross editor' is the wordplay.
'by' says to put letters next to each other.
'cross' becomes 'x' (X is cross-shaped).
'editor' becomes 'ed' (abbreviation).
'a' next to 'x' is 'ax'.
'ax'+'ed'='AXED'
(Other definitions for axed that I've seen before include "Stopped" , "Abandoned or curtailed - using hatchet?" , "Dismissed with a hatchet" , "Dismissed, given the chop" , "Cut; terminated" .)