Cunning that involves group in execution method (10)
I believe the answer is:
guillotine
'execution method' is the definition.
(blade for beheading people)
'cunning that involves group in' is the wordplay.
'cunning' becomes 'guile' (synonyms).
'that involves' means one lot of letters goes inside another.
'group' becomes 'lot'.
'lot'+'in'='lotin'
'guile' placed around 'lotin' is 'GUILLOTINE'.
(Other definitions for guillotine that I've seen before include "Top" , "Device for parting head from shoulders" , "Head-removing device" , "Execution machine" , "limits debate" .)