Use a hot knife. Go to the kitchen, get a knife – any will do – as long as it’s not your mums/wife/girlfriend’s best silver, heat it up over a gas flame so it’s hot, but not red hot. Maybe 300 C? Then cut through the rope. The heat melts and seals it. If it’s too hot, there will be clouds of toxic smoke and possibly flames. Too cold and it won’t cut, so you may need to experiment to get the temp about right.
Second method is cut through it with a cold (ie room temp) sharp knife, then use a cigarette lighter or candle etc to carefully melt and seal the end, gently rolling it with your fingers (careful so you don’t burn your pinkies) to get a nice finish.