The term 'axe' could be misleading. This 'axe' could have a plough, the weight of the tool would be important for breaking the ground.
This from Caroline Malone in her book "Neolithic Britain & Ireland
"The fact that many semi-polished/ground axes are found at random in the countryside rather suggests that cultivation may have been just as important as tree-felling, which is the usual explanation for these tools"