Displeased with one's mongrel (5)
I believe the answer is:
cross
This could be a double definition.
'displeased' is the first definition.
'one's mongrel' is the second definition.
'cross' can be an answer for 'mongrel' (cross breed). I am not sure about the 'one's' bit.
'with' acts as a link.
Can you help me to learn more?
(Other definitions for cross that I've seen before include "Grouchy" , "Annoyed; symbol" , "Irate" , "Angry, hybrid" , "severe trial" .)