what kind of palm is that "ponytail"? if it is a phoenix dactylifera, i.e. date palm tree ( sorry for taking this assumption ) then removing the suckers require taking into consideration the following: case A - if the sucker on base of mother has roots on earth, then the suitable time for removing it from mother when it weighs between 20 - 30 kg, by digging making a rather wide hole until the base of the sucker is clear on the bottom ( cutting roots is no problem) go ahead; and then by using a heavy sharp tool (spade alone might not be enough )try to hit carefully between the mother's trunk and the sucker not to harm any of them, until a clean and save separation of sucker completed. rap roots area with wet fiber until planting. case B- if sucker is located on a high spot on trunk not reaching the ground, then cut the bottom surrounding stubs ( by a saw )until the base of the offshoot is open , then try to support with the help of mother's trunk if necessary a container holding soil to the base of that offshoot , and then water it each time you attend mother i.e. layering that sucker until roots grow say within one year, then you can separate it from mother carefully, and hope happily ever after hth

So you are saying, forget it, chop it off and let it regrow from the base with no hope of re-starting the top as a second plant. So be it. I know that it will regrow with multiple new shoots. Should I let it grow, then select one to be the new top or let it be a multiple? Any advice?

During the warm months, I grow mine outdoors in full sunlight. When they're actively growing, they do best in as much sunlight as you can provide for them. If they don't get it, their newer leaves will droop and look limp. In full sunlight, they arch up and out, with a perky, graceful curve to them. When the temperature starts to drop in the fall, I scale back on watering. If the days are still warm enough, I'll place them outside, bringing them back in at night when the temperature gets below 50ºF. When the days get too cold, I just keep them inside fulltime from then on. I also cut back significantly on watering, letting them practically dry out completely. Don't get any water in the central crown of the leaves, this could lead to them rotting out. Outdoors, I don't worry about this at all. Only when they're indoors. If you water it too much during the winter months, your ponytail palm will try growing new leaves, which will become limp and flat because of the lower light levels. They'll do just fine in a shaded location. I keep mine on a glass table that only gets minimal light and it doesn't phase them one bit. Just remember to keep them on the dry side, or else they will try growing. Other than that, they'll gladly tolerate a low light, shaded location during the winter. In other words, during the summer months, I keep them in full sunlight and water them quite often. During the winter months, I bring them back indoors, place them on display on my glass table and practically forget about them until Spring. You can see in the photo, the table isn't even next to a window. They only get minimal indirect light all winter long and they do just fine. Oh yeah, one more thing, the tips of the leaves sometimes turn brown. If they do, don't trim them, because it'll just die back some more again.

Depot and show us a pic of the roots. Your Beaucarnea recurvata's problems normally start there. Overwatering will certainly lead you there, as well as being in soil that isn't porous enough.