To see an axe in your dream implies that you enjoy holding power over others. It represents negative emotions such as aggravation, aggression, and disappointment. It is possible that you have the desire to confront someone over an unresolved issue.
To dream that you are chopping wood in your dream indicates that you should dissect your challenges so that they don't seem so overwhelming. Problems may be easier to solve if they are separated into more manageable obstacles. It may also represent a reduction in your ability to dominate and manipulate others.