One's mad having lost this cleaning cloth (3)
I believe the answer is:
rag
I believe this clue is a double definition.
'one's mad having lost this' is the first definition.
(reference to losing one's rag)
'cleaning cloth' is the second definition.
(Other definitions for rag that I've seen before include "Cloth; bait" , "Second-rate newspaper" , "Piece of music" , "Tatter; make fun of" , "Torn piece of cloth or university japes" .)