Narrow escape from weapon, one that cuts head (4,4)
'narrow escape' is the definition.
'weapon one that cuts head' is the wordplay.
'weapon' becomes 'arm' (synonyms).
'one' becomes 'I' (Roman numeral).
'that cuts' means one lot of letters goes inside another (some letters cut their way into other letters).
'head' becomes 'ness' (ness is a headland).
'armi' inserted inside 'ness' is 'NEAR MISS'.
'from' acts as a link.
(Other definitions for near miss that I've seen before include "Almost successful shot", "not a success", "Narrowly-averted accident", "Attempt that just fails to be successful", "Not quite on target, but close".)