A wood easily cut up, not one proving awkward (10)
I believe the answer is:
eucalyptus
'a wood' is the definition.
(eucalyptus is a kind of wood)
'easily cut up not one proving awkward' is the wordplay.
'not' is a deletion indicator.
'one' becomes 'i' (Roman numeral).
'proving awkward' is an anagram indicator.
'easily'+'cut'+'up'='easilycutup'
'easilycutup' with 'i' removed is 'easlycutup'.
'easlycutup' with letters rearranged gives 'EUCALYPTUS'.
(Other definitions for eucalyptus that I've seen before include "Australasian tree" , "Australian tree yielding gum and oil" , "Evergreen tree" .)