I personally have never heard of them being propagated by cutting, but then I don't have much experience with trying to propagate them at all. I would think that any "sucker" you removed would have to have its own roots to survive. From what I can tell of the suckers that are on my needle palm, they look like they are coming directly from the base of the trunk. I would think that those would be the hardest to root.

Hopefully someone else with a more definitive answer can help more than I.

I am sure others here can answer more thoroughly but from what I know it will not happen unless you get roots too. Palms cannot produce roots from stem tissue. I know some monocots can, but palms aren't one of them. You may try root pruning them and let them sit for a while then try removing them a little later so there is not so much shock.
Go at it like people do when dividing bananas might work for you too. I would think you could remove one at a time and not stress the mama too much. Let's see what others say before you go at it though! I divide a lot of young palms after germinating but really haven't divided established ones.

I have a needle that produced some shoots and even with some roots it is hard to get them to grow,they grow so slow that it took 10 months before I could see they were dead!I am sure if a horse are something a stepped on it and it broke off it would root just fine!

Some people have cut limbs off there needle palms i have planted them there still dark green after 1 1/2 years