Log remark that's humiliating (3,4)
I believe the answer is:
put down
I believe this clue is a double definition.
'log' is the first definition.
(I know that log is a more specific form of the action put down)
'remark that's humiliating' is the second definition.
(a put down is a humiliating remark)
(Other definitions for put down that I've seen before include "Write" , "defeat" , "Slight" , "Make record" , "drop" .)