Big-headed American's vehicle (3)
I believe the answer is:
bus
'vehicle' is the definition.
(public transport vehicle)
'big-headed american's' is the wordplay.
'big' becomes 'bu' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'headed' means to remove the first letter (head can mean to remove the top from something).
'american's' becomes 'a's' (common abbreviation - e.g. in organisation names).
'as' with its first letter taken off is 's'.
'bu'+'s'='BUS'
Can you help me to learn more?
(Other definitions for bus that I've seen before include "Road vehicle able to carry many passengers" , "Charabanc" , "Mode of public transport" , "Public transport vehicle" , "Use transport" .)