One on latrine duty, say, gags, losing heart over work involving one (3,4)
I believe the answer is:
'one on latrine duty say' is the definition.
(term for someone given bad jobs to do)
'gags losing heart over work involving one' is the wordplay.
'gags' becomes 'jokes' ('joke' can be a synonym of 'gag').
'losing heart' means to remove the middle letters.
'over work' becomes 'op' (abbreviation for opus. I am not sure about the 'over' bit.).
'involving' indicates putting letters inside.
'one' becomes 'a' (a thing is one thing).
'jokes' with its centre taken out is 'joes'.
'op' going around 'a' is 'oap'.
(Other definitions for joe soap that I've seen before include "Fellow" , "He's just an ordinary man - but clean?" , "scapegoat" , "dopey sort" , "One saddled with nasty work" .)