Demonstrate core has been removed from testimony (6)
I believe the answer is:
evince
'demonstrate core' is the definition.
'evince' can be an answer for 'demonstrate' (I've seen this in another clue). I'm not certain of the 'core' bit.
'has been removed from testimony' is the wordplay.
'has' becomes 'eats' (eating is a kind of having).
'been' becomes 'sat' (sitting is a kind of being).
'removed from' is a deletion indicator.
'testimony' becomes 'vince' (I can't explain this - if you can you should believe this answer much more).
'eats' with 'sat' removed is 'e'.
'e'+'vince'='EVINCE'
Can you help me to learn more?
(Other definitions for evince that I've seen before include "Make evident" , "Indicate (something)" , "Indicate or display, say a feeling" , "Show or display, say feeling" , "Make clear, show (quality)" .)