Costus barbatus (red tower ginger)

I have moved into a house with these growing everywhere, a huge clump of them I cut to ground level leaving only a few shoots so I could get to other trees growing over house, will they grow back? Have I totally.destroyed them???

 

Highly unlikely to have died barring other factors such as drought or herbicides.

 

Not only is it not dead (barring drought and herbicide, as Saltcedar says), it will likely come back about twice as vigorous in a few months. I almost always give Costus and its relatives (Alpinia, Zingiber) a severe haircut once a year to keep them under control, and that's been my experience. They're very difficult to kill.