I am always finding fishing lines or driftnets on the reefs here. I do not use or take a knife, because you have to have tension on the line to cut it and/or you end up with a nick here or there, always, it seems. My EMT shears. Those are the best. They cut through anthing like butter, with no tension needed on the line.
Even with students, I will cut the lines. The students like helping follow the line and rolling it up. they also get to practice buoyancy skills and movement.
One time, there was a large monofilament driftnet fouled around a buoy at one of the reefs. Corks had some of it floating, but it was draped and wrapped all the way to the bottom of the line too. My DM and I hopped in and swam over to clear it. so the boat could come in. He had just been telling us how much better his knife was than my little scissors. As we swam over, I told him we should start from the bottom and roll it up as we go. He said no. He was starting at the top. Okay. Learn from your mistakes....
I was cutting away and rolling it up, when I saw a shape plummet down beside me. He was wrapped completely in the net, had pulled off his bc, was riding it down, and wrapping himself up even more. You know, current pulls the floaty bits and he was just hacking at it, since he couldn't roll it with one hand and cut with the other, and it wrapped around him.
I grabbed him, cut him free, waited for him to put his gear back on, then pointed at the bottom of the net. He stayed with me and we finished in about ten more minutes. Huge net then smelling up the boat, and one sheepish dm who learned a lesson about clearing line and nets. He now carries scissors. The emt shears cut through anything.