In Hacksaw Ridge the Japanese just let the American soldiers climb up and there appeared to be no defence. The American soldiers were absolutely safe once they climbed down the ridge. The Japanese could shoot since they occupied a higher elevation. So why didn't they cut the ropes?
You can find the answer in many accounts of the specific battle and I recommend watching the documentary on Doss, The Conscientious Objector. It is true that Doss was one of the ones tasked with securing the nets in the first place.
The ridge is much shorter than depicted in the movie and the terrain below it is far from flat so Japanese positions on the hill had a clear view of American movements all the way down to the landing zone. The only time that American troops could not be seen was right at the base of the ridge.
According to survivors anyone sent up to the top of the ridge for reconnaissance prior to securing the nets that was shot and killed. However, in accordance with Japanese tactics at the time, once it was clear what the Americans were doing, the Japanese soldiers waited until a concentration of troops had made it to the top before they opened fire. This was to ensure the maximum amount of casualties and that's pretty much what they did every time the Americans tried to secure the ridge--up to eight or nine times.
As long as those nets remained, the Japanese suspected the Americans would keep using them and putting large numbers of troops right in their line of fire. Though not always followed, this strategy was used in the hopes that the Americans would get tired of the fighting and offer a negotiated peace. Instead it convinced the US that an invasion of Japan would be too costly and the atomic bomb should be used instead. For what is probably the most comprehensive view of the battle from the Japanese perspective, I suggest The Battle for Okinawa by Colonel Hiromichi Yahara.
Keep in mind the movie is based on true events and there can be all kinds of reasons they didn't cut the ropes given the chaos of war and strategic motives of the different sides.
The Battle of Okinawa is known to be one of the bloodiest battles of the Pacific War and the key attack points were the beach and the ridges. The movie makes it seem like the rope ladder was abandoned and left with two guys to guard it at certain points. I find this highly unlikely. If the US took the time to put a mesh rope ladder up, they would leave enough forces to defend it. Any Japanese soldiers that came close enough to the ridge to attempt to cut it would have been gunned down. That said, its very possible that they DID attempt to cut the ropes down and its very possible that they succeeded in some of these attempts.
Ultimately, whether they attempted to cut the ropes or not is a detail not important to the movie's plot.
We are meant to suspend our reality and assume that if any attempts were made to cut the rope, they either failed or were remedied by putting it back up.
According to the true story the Japanese wanted the Americans close to their hideout for tactical reasons. I guess that is part of the reason why they didn't cut the ropes. Another reason could be the exposure to the heavy artillery at sea. Also, according to the true story Desmond Doss was one of the volunteers to climb up and attach the ropes (not depicted in the movie). So it was mounted by the Americans, not the Japanese.
Simple answer the Japanese built that rope latter to get on the hill. However that hill is one way up and down whatever food and supplies the Japanese would get came from the rope so they can't cut it since that is there supply chain. Also why cut the rope if it's a one way up and down. It's make it easy for ambushing since you have the exact location that the enemy forces are coming from. This is all what war is ambushing and counter ambushing.