I am amazed how many people don’t carry knife theses days. This is just stupid!!!
A smart diver should carry two knives, mounted far apart–say, on your calf and your chest–so you can always reach a knife no matter what part of you is entangled. Keep them sharp. Mount them so you can reach at least one knife, preferably both, with either hand. One knife should be a small one with a sharp tip that can get into tight spots.
A serrated edge is most effective on large ropes and thick clumps of kelp and seaweed. Shears or line cutters work best on monofilament.