This is a simple one. What is your favorite rope cutter?
For most of my rope cutting chores, I have a custom everyday carry sheath knife. (Made by me.) It is always handy and I’ve yet to fail cutting what I need to.
Depending on what material the rope is made of, I also have on hand a lighter and some small string from the core of some paracord with which to whip the ends.
SS
Whatever sharp knife is handy. A small EKA folder, a Mora, etc. For details on fancy knot-work one of the smaller “dynema” shears is good
do tell, roo 
i am a fan of a single-edge razor,
has a folding handle and uses disposable blades,
a double blade snapped in half.
i can sharpen a blade about 3 times as well
(sharpening steel)
paracord up to 4mm is all i use
very cool to make knives,
i’ve never endeavoured,
but there is a cleaver in the queue that i plan to restore,
the handle is monstered,
warped beyond warped,
i’m not sure if it’s the original handle (wooden sides).
if it isn’t, i wonder what happened to it.
the blade has an australian stamp ‘GREGSTEEL’
Since I tend to grab any lousy cutter that happens to be around, I was hoping to get inspiration from the community. I do have a Sencut Sachse on order for general-purpose use, but I haven’t tried it yet.
There are always folding marlinspike knives. Some are quite well made and the spike could come real handy if you snug a knot too tight.
Since I have a plethora of knives I have made and I tie mainly using synthetic materials, I personally would opt for a heat cutter. Then again, I don’t cut all that much rope, and cords are easy enough to melt the ends of (or whip).
The main thing is to cut on a surface that will not damage the edge of whatever you end up using to cut with.
Not exactly about knifes but since the cutting board was mentioned…:-)
Wrapping (tightly) the rope with an electrical tape and cutting through it makes the cut easier and nicer, likely because the fibers have less chance to move around as they are being cut - it feels more like cutting a solid and I would even argue that it allows for using less-than-razor-sharp blades and still getting a nice cut.
I always carry an Olfa Magnatouch in my pocket - its small, light, sharp and very cheap - and unlikely to cause offence if used in a public place - unlike a fixed blade knife which is almost certainly illegal to be carried in the UK. At home I tend to use a fixed blade cutter (basically a handheld blade and anvil arrangement very like many pruning tools). This has an easily replaceable blade for rope or heavy cord as well as thinnish wood.
engrave or stamp your knives !
thankfully i only need three stamps (A,L,N), but anyway i know of a couple of times they would’ve gone ‘walking’ if they hadn’t been stamp identified 
and i know of one that hadn’t been stamped and … i don’t have it anymore
I just want to share the joy of being recently introduced to a friendly Opinel #8. It may need to grow on you if you’re used to more scary-looking knifes, but try it and you may not regret it…
additional 2c : sharpen your knives yourself,
or take them to reputable sharpener,
not to the travelling knife sharpener 