I drop, say, useless person with hesitation - a sad thing (4-6)
I believe the answer is:
tear-jerker
'a sad thing' is the definition.
The definition suggests a singular noun which matches the answer.
'i drop say useless person with hesitation' is the wordplay.
'i drop say' becomes 'tear' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'useless person' becomes 'jerk' (term for a stupid or inept person).
'with' means one lot of letters go next to another.
'hesitation' becomes 'er' (sound used when hesitating).
'tear'+'jerk'+'er'='TEAR-JERKER'
Can you help me to learn more?
(Other definitions for tear-jerker that I've seen before include "Highly sentimental story, film etc" , "Extravagantly sentimental book, play, etc" , "Tragedy perhaps" , "Weepie" , "tale that's emotional" .)