Give out when Americans mock show of appreciation (10)
I believe the answer is:
distribute
'give out' is the definition.
(synonyms)
'mock show of appreciation' is the wordplay.
'mock' becomes 'dis' (both can mean to make fun of or insult).
'show of appreciation' becomes 'tribute' (I can't justify this - if you can you should believe this answer much more).
'dis'+'tribute'='DISTRIBUTE'
'when americans' is the link.
I am not very happy about this link. Some or all of it may be part of another bit of the clue.
Can you help me to learn more?
(Other definitions for distribute that I've seen before include "Supply" , "Pass round" , "Deal out" , "Give out" , "Hand or share out" .)