These are OK: (A) He chopped with an axe. (b) He chopped down the tree with an axe. (c) He chopped the tree using an axe.
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Vincent Teo(i) Is that wrong if I use "...by using the axe"?It isn't wrong; it's just more than you need to sound natural.
(ii) Is that clear in meaning if just say "...chopped (the tree) with an axe"?