Mr Sitwell, who also appears as a critic on the BBC programme MasterChef, suggested journalist Selene Nelson pen a series of articles about force-feeding meat to vegans, whom he accused of “hypocrisy”.
Ms Nelson had suggested a regular series on vegan cooking, featuring recipes, commentary and news.
In an emailed response to her pitch last week, the magazine editor wrote: “Hi Selene. Thanks for this. How about a series on killing vegans, one by one. Ways to trap them? How to interrogate them properly? Expose their hypocrisy? Force-feed them meat? Make them eat steak and drink red wine?”
In a statement, Waitrose & Partners Food Magazine said it believed that it was the “right and proper move” for Mr Sitwell to step down as editor.
The statement said: “We have been informed by John Brown Media, who produce the Waitrose & Partners Food Magazine, that William Sitwell is stepping down as Editor of Waitrose & Partners Food magazine with immediate effect.
“In the light of William’s recent email remarks, we’ve told John Brown Media that we believe this is the right and proper move - we will be working with them to appoint a new editor for the magazine.
“We have had a relationship with William for almost 20 years and are grateful for his contribution to our business over that time.”
Ms Nelson said she had been shocked by Mr Sitwell’s email.
She told BuzzFeed News: “I’ve never seen anything like it. I’ve written about many divisive topics, like capital punishment and murder cases and domestic violence, and I’ve never had a response like that to any of my articles or pitches.
“And he’s the editor. He’s representing Waitrose and he’s talking about ‘killing vegans, one by one’?”
She added: “If William Sitwell wants to continue eating meat and hating vegans, that’s his prerogative, but to have this attitude towards others when he’s representing Waitrose is seriously bizarre.”
The upmarket supermarket launched a new vegan range earlier this month.