Stingy type put down unfinished drink (9)

'stingy type' is the definition.
Although both the answer and definition are singular nouns, I cannot understand how they can define each other.

'down unfinished drink' is the wordplay.
'down' becomes 'humble' (I can't explain this - if you can you should believe this answer much more).
'unfinished' means to remove the last letter.
'drink' becomes 'beer' (beer is a kind of drink).
'beer' with its final letter taken off is 'bee'.
'humble'+'bee'='HUMBLEBEE'

'put' is the link.

Can you help me to learn more?