An axe is primarily for cutting things down or for cutting them into smaller units. It is also a formidable weapon; so what part is the axe playing in you dream? See: weapons.
Idioms: Axe to grind; to be axed lose one’s job.
Useful Questions and Hints:
Does this represent a power or authority?
Am I ‘chopping’ an idea or situation or even myself into smaller parts?
What am I using the axe for – or what is my relationship with it?
Use Processing Dreams.