The boozer now sports the name 'Heworth Inn' after new landlady Leah Stannard decided the old moniker was too meaty.
Stannard also added a new menu - with a third of all dishes being vegan and vegetarian-friendly.
Vegan and veggie cuisine
"As we are going to have a really keen focus on vegetarian and vegan cuisine, we think it is a tasteful, sympathetic and reasonable decision," said Stannard.
"We want to have an excellent vegetarian and vegan offering, so found the name slightly compromising of the idea. We imagined that many brides may not want the invites for their big day to be at a place called the Shoulder of Mutton.
"We have taken into account the area's and the building's heritage and have consulted various conservation bodies in the area and received warm feedback and support for the new name."
Not everyone was happy about the news. One social media user wrote: "FFS ……. Grow up! Tradition itself will soon be outlawed if these individuals are allowed to continue."
Another added: "Shame something like the name of a traditional pub has to change just because somebody doesn't agree with it.
"There are a lot of things I do not agree with but won't get changed, so things like a name of a pub with a non-discriminatory name should be left alone."
But the move has been met with praise from some quarters. Dominika Piasecka, of The Vegan Society, released a statement saying the change signaled a 'positive direction, as eating animals is increasingly becoming an outdated practice'
"We've heard of a couple of businesses going out of their way to exclude or annoy vegans, so it’s nice to see the opposite happen for once," she added.
"The number of vegans in Britain has quadrupled in the last four years and many businesses are taking catering for them seriously, with plant-based food being inclusive not just of vegans but everyone else as well."