I've run D&D without magic. It technically works, but there's a lot missing.
TLDR: The easy way is to cut all classes/subclasses/races/subraces that are too magical for your setting, and to fluff any remaining magic (e.g. monk ki, artificer spellcasting) as being mundane. Provided most of the problems have mundane solutions then the campaign will function, but there will be some voids in the design space (mainly mental attributes being unimportant).
The hard way is to redesign or replace all spellcasting classes with fully-featured nonmagical equivalents. This is not as simple as swapping Spellcasting for some other feature; the spellcasting classes will need to be rebuilt from the ground up or replaced entirely.
Or you could follow Groody's advice and use a different system better suited to the campaign you are trying to run.
I've run a D&D campaign without magic. It was a medieval-esque setting rather than a cyberpunk setting. The story pitted a nonmagical imperial military against a magical fey incursion, with the player characters' lack of magic providing contrast with the fey and emphasising the fantastical nature of magic.
I banned classes, subclasses, and races with overtly magical powers. This restricted the class selection to Fighters, Rogues, (Berserker) Barbarians, and some Monks (for Tier 1 and 2 you can pretend Monks are non-magical; Way of the Open Palm and Kensei are obvious choices, although a player persuaded me to allow Way of Mercy which we fluffed as acupressure and rapid first aid). Elves, forest gnomes, tieflings, and dragonborn were out, but other PHB races were fine.
The game was "balanced", in the sense that all remaining options were still viable. The campaign was successful and my players enjoyed it. However, there are a few caveats.
You obviously cannot rely on your players having any magical solutions to problems. As long as most of the problems you present to your players are mundane in nature, they should be able to use mundane solutions. But if you drop a forcecage on the party then obviously they will have a bad time.
Healing is almost non-existent outside of magic. My party had a Way of Mercy monk, and I really appreciated having a healer like that. Besides that, someone could take the Healer feat. Otherwise, you may need to homebrew some other healing solutions. I included some healing remedies which recovered hit points over a few minutes, to allow for faster healing between encounters.
You would want to be careful about using monsters which are resistant/immune to nonmagical damage. Monks can bypass this, but other classes cannot. You will want to provide another way to overcome the resistance/immunity (in my campaign, it was iron/steel, because fey), or not use that resistance/immunity.
The biggest shortfall, though, was that scrapping most of the classes meant the mental attributes (INT, CHA, WIS) were less relevant because they were not primary stats. The game still technically worked without those stats, but I could feel the asymmetry. Removing the casters left a void in the design space. If I were to run the campaign again, I would introduce some homebrew/third-party classes to fill the void (such as Kibbles' Warlord).
All these problems are a symptom of D&D having been built with magic as a ubiquitous feature. While the rules work fine without magic, and each class in 5th edition is able to stand on their own, stripping out magic leaves some big holes in the design space.
You have the benefit of working in a cyberpunk setting. Unlike my medieval-esque setting, cyberpunk has a bunch of technology which can reasonably approximate a lot of magic. Advanced technology can fill the space of magic items. Artificers already have their spellcasting flavoured as them using technology so artificers could probably be used as-is. Bards and clerics probably won't work as-is, though, so you would need to find a suitable substitute.
I'll add that I've also been a player in a steampunk Pathfinder campaign without magic (which also pitted the nonmagical people against an extraplanar magical incursion of elves). In this case the GM carefully homebrewed almost every class and race to be fully-featured without magic and to interface with the urban steampunk setting. The campaign worked excellently, but that full redesign was important, and the GM was tweaking on the fly as we tested things.
In all this, you need to consider why you are using D&D. In my case, it was because I wanted to see what happened when the players were stuck at the pointy end of the magic wand (so I still needed a magic system), and while I was running very low fantasy it was still fantasy. But running cyberpunk without magic has essentially no similarities with D&D. If all you have left is the bare bones of the mechanics and none of the genre or style, you might be better off hunting for another system which better reflects the campaign you want to run. If you still want to run D&D this way, go for it; we learn by trying. But this might be a good opportunity to branch out to another system.