This happened on my BX a couple of months ago, only I didn't hear it and the flailing rubber eventually wore it's way through the plastic wire loom and the wires beneath, taking out power to the fuel lift pump and blowing a fuse.
So yeah, you need to cut the rest of it off, and yes, you should replace it since it keeps dirt out of the CV joint on that end of the drive shaft.
The rubber boot is cheap enough from Messick's. The labor is a little tough, since you've got to undo two pairs of three bolts that hold the CV coupler together, and space is tight. Worst for me was getting cir clip back on the end of the driveshaft, but getting the coupler back in place, fighting the spring compression, took some creative cursing too.
While you in there, you will may find that the four small "ring dampers" underneath the four ball bearings in the CV joint have been damaged, so you might as well order replacements for those as well. Here's what I purchased, including a spare boot and an extra ring damper:
Kubota K2561-14130 (COVER, JOINT) Quantity: 2 $1.84 each $3.68
Kubota K2561-14140 (CIR. CLIP, EXTER) Quantity: 1 $0.62 each $0.62
Kubota K2581-14160 (RING, DAMPER ) Quantity: 5 $0.42 each $2.10
Note mine was for a BX1870, so a different engine. Pretty sure these parts would be the same, but you might want to double check.
As for instructions, I'd search for YouTube videos that detail replacing the HST Cooling fan. That's at the other end of the driveshaft, but most of the videos show taking apart the CV joints at either end, and the joints are pretty much the same in any case. For your repair, you won't need to touch the fan end.
Good luck!