Will this grow new shoots?

Hi Guys,

I have had this plant for 3 years and its got a bit wavy and difficult to accommodate.
I already cut one of the branch things off because it was well out of wack, if I cut another off or both, will it shoot again or just die?

Also does anyone know what its called?
Thanks

 

yes it will shoot back from a main stem.. it is Yucca guatamalensis (syn. elephantipes)

 

It's best to prune them in early spring.
You should cut the branch off about 4" from where it joins the main stem. It should then reshoot from that point.

 

Thanks for the replies. I might just keep it now