Cut just a small part of the lawn (4)
I believe the answer is:
sawn
'cut' is the definition.
(cut with a saw)
'just a small part of the lawn' is the wordplay.
'just' indicates an anagram (I've seen this in other clues).
'small' becomes 's' (abbreviation - e.g. clothes size).
'part of the lawn' becomes 'wn' (I am not sure about this - if you are sure you should give a lot more credence to this answer).
'a'+'s'='as'
'as' anagrammed gives 'sa'.
'sa'+'wn'='SAWN'
Can you help me to learn more?
(Other definitions for sawn that I've seen before include "Severed" , "(Of wood) cut" , "went up and down?" , "Cut with serrated blade" , "timber must be" .)