This is an interesting but thought provoking question. I don't think I've ever came across one like this before. The short answer is no. For various reasons.

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1. Egypt's most vicious rivals were not to the south but primarily in Asia or Eurasia. they reserved almost all of their hate for them historically and fought the overwhelmingly vast majority of their wars against them. As the Nile flows from the southern states deeper in Africa into the North through Egypt then emptying into the Mediterranean, they never managed to anger any of their southern neighbours enough for them to attempt to kill all Egyptians.
2. The people who lived directly to the South of Ancient Egypt throughout history were essentially like a mirror civilization to them. There are more pyramids in Sudan than Egypt, there is an abundance of hieroglyphics and hieroglyphic style writing in Sudan (we have not yet decoded it), they were essentially a very similar culture, language and peoples, who really only difference were political entities, they even shared religions, custom and worship of the same gods throughout history. The Ancient Egyptians believed their origins laid at where the gods were born which was the foothills of the "springs of the nile". While the research in this area is complicated and not completely understood by Egyptologist for a variety of factors, mainly dealing with the Aswan dam flooding South Egypt and North Sudan in an archaeological rich zone, and all the wars and dictators in Sudan who are essentially distrustful (with good reason) of Westerners claiming to be digging for artefacts (there is a history of spies pretending to be archaeologist and aid workers and photographers). We do know they were very similar cultures and peoples.
3. South of the Sudan, the distance would be enormous and the Egyptians would have had at best limited and little contact beyond traders and scholars with the other groups like Ethiopia and D'mt, etc. empires simply due to distance.
4. You also have to understand the time periods we are talking about. You have the Kerma civilization in Sudan and they last from 2500 bc to 1500 bc. The technology at 1500 BC in the world wasn't exactly extremely advanced as far as dam building goes. People never really thought of using dams as a weapon in general, and the Kerma people probably had no such desire to do so against the Egyptian people because they are too close cultures.
5. You have to understand that ancient Sudan was very big, it basically encompasses almost all of modern sudans, around 2.5 million km, it was bigger than Egypt's New Kingdom by land area by several times and had more fertile land, it was even bigger than most ancient empires including being almost as big as the Byzantium empire at its height which was around 2.8 million sq km and that was 500 ad not 1500bc. And as you know the Byzantium empire split from the Western Roman empire because the Romans basically thought it was too big and hard to govern such a large territory. So the Sudanese would have had their hands more than full trying to govern such a large territory and trapped between two powerful kingdoms, Egypt to the North and Ethiopia to the south.
6. Dam technology was not advanced enough to build a dam to complete re-route such a massive river. To put it in perspective, when the Jones Falls Dam on the Rideau Canal in Canada, which was considered a state of the art dam in 1831 was only about 60 feet tall. You'd probably need at least 100 feet to have any success in the dam, and the first one of those on the Nile came in the late 1800s or early 1900s with the Aswan low dam. Mind you, we are talking about redirecting the river entirely, not just slowing its flow, so you'd really need modern technology.
7. By 1500 BC the Egyptians started invading as the Kerma nation grew weaker internal rebellions and splits and things like that. They eventually fought for their freedom emerged as the Kush civilization who would go on to rule Egypt.
8. Part of your questions also kind of ignores the dynamics of Sudan and how dams work. A dam basically slows the flow, it doesn't stop it. It can be used to stop flooding in an area, save water, or generate electricity. However, all that water has to go somewhere. The most fertile areas of Sudan are along the Nile, just like Egypt. To dam the Nile means you have to essentially, flood these super fertile areas with water making it useless for agra purposes because it'd be under 100-200 feet of water. This would likely precipitate mass starvation and hunger in the region as people get angry about having no food and others are angry you flooded their land. You'd need to essentially redirect the water of which a dam could be useful but would not be essential.
9. This could work, but the redirecting of the water would carry its own issues, you'd need to essentially buy up land from locals who will agree to this, then dig a giant moat that slopes downward from the Nile to the red sea that reaches the ocean. Employ probably millions of people to do this and hope you don't encounter any type of rock you cannot dig through with 1500bc tools. And as the Iron age did not happen yet, and you are in Sudan you'd probably be using softer bronze tools. So why didn't the Sudanese just dig this giant moat anyways?
10. The Red Sea Hills would have been a massive barrier to this plan. Atbara, which is probably the closest settlement to the Red sea along the Nile in Sudan is at an elevation of 350m, the heighest Red Sea Hill is at an elevation of over 2100 meters. So you are basically trying to send water uphill. And these hills are basically like mountains in appearance and size. Its not like 1 or 2 or 20 hills, it is an entire range of hills, that looks much more like a mountain than a hill and is around 120-200km wide/deep. So at this point you are basically talking about tunneling through a volcanic rock mountain with bronze age tools for hundreds of KM. Here are somepictures to give you an idea.
11. 📷 https://egyptsites.files.wordpress.com/2010/09/pc049387.jpg?w=584
12. 📷 https://cdn.cnn.com/cnnnext/dam/assets/190826130501-red-sea-mountains-full-169.jpg
13. Lets not speak in delusional terms, it wasn't going to happen with the technology of the time.
14. Even if they somehow did manage to do, ok, you turn Egypt dry forever and kill all the people. Besides creating a refugee wave running into Sudan by the millions your army cannot stop who have nothing to lose and are dying of hunger. What have you achieved? The ancient people of Sudan had traded heavily with Egypt, despite the wars they had, it didn't actually benefit them to wipe them out.
15. The question is almost like asking, why didn't the allies just murder all the Germans after ww1 or ww2. Sure, they could have done it, they had the means to do so. But the allies had bigger plans, and profit motives, etc. The Sudanese viewed the Egyptians as useful because they essentially fought and weakened every invader who potentially threatened Sudan from the North (every Asian and European invader) and served as an early warning system. Unlike Egypt, Sudan barely got any invasions and the few that did occur largely failed or fizzled out before the invaders could get deep into their territory until the 1800s AD when ottoman egyptians invaded Sudan. There was also another time in the ancient period where this occurred. In comparison Egypt was essentially colonized or occupied and invaded almost continuously from 600 BC until the 1950s.
16. Egypt was basically a buffer for Sudan to stop Eurasian invasions. Why would they take out their buffer, doing all their fighting? After Alexander the Great Invaded Egypt and learned that much of its wealth was coming from the south in Sudan, he sought to invade it, but because of the war they had with Egypt, the Sudanese had already assembled an army of 80,000 including thousands of war elephants so Alexander backed down and invaded further East.