Straight edges

If you are asking if a straight (plain) edge knife can cut rope, the answer is yes.
However, if that rope is wet and slippery, a serrrated edge will cut it much better.
 
Plain or straight edges were by far the most common throughout history and I dare say more rope was cut in days long past than currently. Sometimes after we started using metal for blades the serrations stopped for a while. Knapped stone and volcanic glass blades were pretty much always serrated before we figure out metals.
 
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