Be off with you! That's scornful, not half (4)
I believe the answer is:
scat
'be off' is the definition.
Although both the answer and definition are singular nouns, I cannot see how they can define each other.
'you that's scornful not half' is the wordplay.
I cannot really understand how this works, but
'that's' could be 'sc' and 'sc' is found in the answer.
The remaining letters 'at' is a valid word which might be clued in a way I don't understand.
This may be the basis of clue (or it may be nonsense).
'with' acts as a link.
Can you help me to learn more?
(Other definitions for scat that I've seen before include "Jazz-singing" , "Wordless jazz singing" , "leave quickly" , "Leave; jazz singing" , "Jazz singing - animal droppings - silvery fish" .)