I would also suggest that the contrasting of the improvisation of the rope with the lengthy process of execution that would lead to axes is used by Atwood to emphasize that Mary was hanged hastily and without any sort of fair trial. She was accused and executed on the same day, as far as I can tell from the poem. The rushed process led to a simple execution style. The process of her execution was rushed and the mob was out to kill Mary based on accusations of her being a witch. It seems that mob mentality won over in this one.
The poem "Half Hanged Mary" deals with the botched execution of Mary Webster of the 17th century who was accused of being a witch. The lines "The rope was an improvisation/With time they'd have thought of axes" occurs in the second section of the poem.
It was a lot easier hanging Mary: all you needed was a rope and a tree to hang her from. It was done readily without any preparation. The greatest advantage of death by hanging is that no blood is spilt and hence the execution is not messy.
On the contrary, execution by beheading with an axe would require the trained services of a professional executioner who should be able to accurately chop her head off with one neat stroke. It cannot be done with an ordinary axe which is used to cut wood. A particularly heavy axe had to be manufactured specially for this gruesome purpose. Needless to say it would have been very messy with blood splattering all around the place.
But, as Atwood remarks very grimly, this was only the beginning and that eventually as the people became more and more bloodthirsty they would institutionalize the execution of 'witches' by beheading.