Strict American cuts a tree by mistake (7)
I believe the answer is:
austere
'strict' is the definition.
(I've seen this in another clue)
'american cuts a tree by mistake' is the wordplay.
'american' becomes 'us' (abbreviation for United States).
'cuts' indicates putting letters inside (some letters cut their way into other letters).
'by mistake' indicates anagramming the letters.
'a'+'tree'='atree'
'atree' anagrammed gives 'atere'.
'us' inserted into 'atere' is 'AUSTERE'.
(Other definitions for austere that I've seen before include "Grim - USA tree (anag)" , "Severe in manner" , "Severe, ascetic" , "Without luxury or ornament" , "Spartan and abstemious" .)