Has half a mind to reduce service, the pennypincher! (5)

I believe the answer is:
miser
'has half' is the definition.
Although both the answer and definition are singular nouns, I don't understand how they can define each other.
I cannot understand how the rest of the clue works.
Can you help me to learn more?
(Other definitions for miser that I've seen before include "we may find boring" , "One hoarding wealth" , "screw" , "One hoarding money" , "Cheapskate" .)
