I hang limbs while in a bucket tens of times a day. I keep a half inch by 6 to 8 foot (also 3/4 ") on the bucket floor with a spliced end I buy from TStuff but I have to shorten them for expediency for a shorter tail. I girth hitch the spliced eye to the stub that will remain and then sometimes a marl then a r. bowline or timber hitch to the piece being cut on the butt. I then cut between the girth hitch and the tie off after moving it around for the bottom cut.
I then one hand all over the hanging piece often stabilizing the piece from swinging with the other hand, sometimes just holding and tossing pieces. You have to be careful because the big piece is swinging around. You can't do this very well climbing because you can't get to the canopy of the hanging piece. Why do you do this? Because the piece being removed is hanging over a roof, patio etc. and when you hang it, now it is hanging over nothing, and you have a safe drop area. Speed...speed.