A cross English teacher's cutting equipment (3,5)

I believe the answer is:

axe heads

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'a cross english teacher's cutting equipment' is the definition.
I can't tell whether this definition defines the answer.

'a cross english teacher's' is the wordplay.
'cross' becomes 'x' (an X is a cross).
'english' becomes 'E' (abbreviation as in OED).
'teacher's' becomes 'head's'.
'a'+'x'+'e'+'heads'='AXE-HEADS'

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I've seen this clue in The Guardian.

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