Mineral one's cut with axes (4)
I believe the answer is:
onyx
'mineral' is the definition.
(onyx is a kind of mineral)
'one's cut with axes' is the wordplay.
'cut' means to remove the last letter.
'with' says to put letters next to each other.
'axes' becomes 'yx' (Y axis and X axis).
'one' with its final letter taken off is 'on'.
'on'+'yx'='ONYX'
(Other definitions for onyx that I've seen before include "Stones" , "Stone-like marble with coloured layers" , "African antelope" , "Kind of agate" , "Banded chalcedony" .)