If you leave some growth/sprouts on the plant, it will come back.

You can start new plants by sticking chunks of cane into dirt; keep the original top up for best results, though planting it sideways can also work.

I don't know what happens if you cut it to the ground, but now that you mention it, I'm going to try it on that %$! plant my husband put too close to the path.

When sugarcane is harvested it's cut to the ground. The base of the plant resprouts. Cuttings are really easy, you can leave them in water until they have a good root mass, or just in damp soil.