Poor dog, its appropriate part cut short (7)
I believe the answer is:
curtail
'short' is the definition.
(thesaurus)
'poor dog its appropriate part cut' is the wordplay.
'poor dog' becomes 'cur' (I've seen this before).
'its' becomes 'til' (I can't justify this - if you can you should believe this answer much more).
'part' suggests taking the first letters.
'cut' indicates putting letters inside (some letters have cut into others).
The initial letter of 'appropriate' is 'a'.
'til' going around 'a' is 'tail'.
'cur'+'tail'='CURTAIL'
(Other definitions for curtail that I've seen before include "Abbreviate" , "Dock" , "Shorten, abridge" , "Cut short like canine appendage" , "Cut short (an activity)" .)