The problem is that my usual answer is: you can’t. It’s like soy milk. You can CALL IT milk all you want, but it’s juice. Because soybeans don’t have nipples. You can try to run a low-magic D&D game, but you probably have to break D&D to do it. And it wouldn’t be D&D.
I've never bought into the idea what "D&D" is as it changes every edition. Older editions of D&D were definitely "low magic" compared to 5th Edition at low levels. That doesn't make them the soy milk of D&D. So the idea that down-tuning D&D means it is no longer D&D is patently absurd. It might not be
5th Edition D&D, but that's not an inherently bad thing. 5th Edition is as riddled with design flaws as all of its predecessors. Suggesting that D&D is either 5th Edition or "you might as well play Conan" is fairly daft. And I love Conan. Besides, there are a
ton of better suggestions for D20 retro-clones or red/white/blue-box inspired games like Dungeon Crawl Classics, LotFP, etc. So why do people try to make Low Magic versions of 5E? Because people own 5E and they know 5E. You can scale back the rules for 5E and still use the Monster Manual, for example. Or the published campaigns. You just reset expectations for damage output and you work in more resource management. These things exist in the game already. People just ignore them.
There has been a
marked difference in what we call D&D. So eliminating cantrips doesn't suddenly turn the world on its head and De-D&D the game. It just means that spellcasters get reverted back closer to their 1st and 2nd Edition counterparts. Low power at low-levels. Wizards become forced to approach some problems as mundanely as their counterparts occasionally. And let's be real for a second: People
played D&D during those editions, so clearly there is just a difference in expectations in the modern game. Some players may like the new way, some may like the old way. Wizards of the Coast has made the changes to the game they thought would best benefit their revenue and profit margins. Has nothing to do with defining what D&D is, or is not. Even Gary couldn't pull that off. And given how plentiful Ability Scores points are and how great Dexterity is, it's actually
easier to make a Cantrip-Free Wizard than ever before and still contribute at low levels.
As far as I'm concerned, as long as you have a medieval-ish fantasy game with D20s, hit point abstractions, SDCIWC ability scores, Fighters/Clerics/Rogues/Wizards and fantasy races, etc you're still playing D&D. Doesn't matter if your wizards are low power, or high power. If your hauls are small or Monty.