Cut head off...cut head off exotic flower first (7)
I believe the answer is:
execute
'cut head off' is the definition.
'cut head off exotic flower first' is the wordplay.
'head off' suggests taking the first letters.
'flower' becomes 'exe' (Exe is an English river**).
'first' is a charade indicator (letters next to each other).
The initial letter of 'exotic' is 'e'.
'cut'+'e'='cute'
'cute' put after 'exe' is 'EXECUTE'.
(Other definitions for execute that I've seen before include "Realise" , "Maybe send to chair" , "Put to death - put into effect" , "Carry out - official killing?" , "Carry out; behead" .)