I've climbed for years, there is NOTHING like running a saw 150+ feet up a tree or dropping a 2' foot thick top on a windy day before blocking down big chunks.
as for cutting a rope at height, better be sure to know which rope your cutting, especially when you are under duress, tired etc.
If the rope is TENSIONED (like a bull rope), simply touching an edge to the rope will blow it. same if its your lifeline and its tensioned. You want to be extremely careful in your cut.
I carry and recomend the Spydie Rescue Assist, both because its blaze orange and easy to find if you drop it in the woods, but also because the serrations rip thru doublebraided ropes no matter the thickness. It also has a built in whistle, which i will attest DOES work to alert people. Its also ROUNDED at the tip.
I highly recomend NOT using a FIXED BLADE. Main reason is if you cut a line, and suddenly swing free, you can stab yourself. A cut or stab at height is extremely dangerous, not to mention distracting, which may cause you to lose control of your descender, etc. Another reason a fixed blade is a nono in the trees, if you drop the knife you risk killing your groundcrew if they are in the drop zone. The point WILL drive thru their neck, shoulder, face, head. There was an incident about 12 years back where this happened, a Buck 119 was dropped from 180' up and impaled the shoulder of the ground guy. Surgeons removed the blade from inside his ribcage, it drove clean thru.
just to let you know, the number of times a tree climber has had to cut a rope in an emergency in the USA and Canada, is in the neighborhood of around 20 , in the last 60 years. It is extremely rare to need to cut a rope up high. Ground crews on the other hand, cut ropes a lot (little inside joke about groundsman running saws around ropes...)