Lop off eel's head? That's harsh! (6)
I believe the answer is:
severe
'harsh' is the definition.
(I've seen this before)
'lop off eel's head?' is the wordplay.
'lop off' becomes 'sever' (I've seen this before).
'head?' suggests taking the first letters (I've seen 'heading' mean this (head could mean the top letter)).
The initial letter of 'eels' is 'e'.
'sever'+'e'='SEVERE'
'that's' is the link.
(Other definitions for severe that I've seen before include "Strict, stark" , "Strict, hard" , "Taxing" , "Grave" , "Drastic" .)