Did you know that you can cut rope with rope? If you have nothing else to cut the rope with you can use friction to cut one rope with another. This is how you do:
Stand with both feet about 20 to 30 centimeter apart on the rope you want to cut.
Slide another rope, or another part of the same rope, under the first rope between your feet.
Hold the two ends of the second rope in one hand each and quickly grind by alternately pulling the ends back and forth while keeping the tension of the ropes.
The rope will quickly snap.