From my research I'm seeing mixed information.
Is there a reason for wanting to cut down one of the plants? If it is due to the health of the plant, it likely would cause further stress and the plant may not survive or continue to struggle.
I have found some reports of people successfully cutting down a stem and it growing, it will likely have multiple green shoots and may not be the growth pattern you desire.
If you do cut this Ponytail I would advise painting the cut end with cinnamon. This acts as a natural fungicide.