It cuts tax, giving rise to unbecoming jocularity (6)
I believe the answer is:
levity
'unbecoming jocularity' is the definition.
'it cuts tax' is the wordplay.
'cuts' indicates putting letters inside (some letters cut their way into other letters).
'tax' becomes 'levy' (I've seen this before**).
'it' placed into 'levy' is 'LEVITY'.
'giving rise to' is the link.
(Other definitions for levity that I've seen before include "Disrespectful treatment of a serious matter" , "Playfulness" , "Frivolous jocularity" , "Disrespectful humour" , "thoughtlessness" .)