Mirth of liberal offspring losing head (8)
I believe the answer is:
laughter
'mirth' is the definition.
(mirth is laughter or cheer)
'of liberal offspring losing head' is the wordplay.
'of liberal' becomes 'l' (I can't justify this - if you can you should give a lot more credence to this answer).
'offspring' becomes 'daughter' (daughter is a kind of offspring).
'losing head' means to remove the first letter.
'daughter' with its initial letter taken off is 'aughter'.
'l'+'aughter'='LAUGHTER'
Can you help me to learn more?
(Other definitions for laughter that I've seen before include "end of the comedian" , "Manifestation of amusement" , "Infectious thing" , "Sign of amusement" , "Cackling" .)