The blogging site, which has more than eight million UK users, said that thousands of pages would be removed in a strategy that has been welcomed by eating disorder campaigners.
However, some Tumblr users have claimed that the blogs work like therapy for users, and removing them would strip away that support community.
According to BBC Newsbeat, Tumblr's Mark Coatney said that blogs about self-harm, anorexia or bulimia are "not a good thing" for the online community.
He explained that it was impossible to remove all mentions of such topics, but the "core" of blogs about them would be taken down.
Coatney said that Tumblr wanted to provide a healthy and supportive environment for users, linking them to organisations that can offer help.
"When people search for certain tags such as 'pro ana', (pro-anorexia) we are going to include messages about why this is harmful and suggest where they can go for resources to help them out," he said.
The move has been welcomed by charities. Susan Ringwood, the chief executive of eating disorder support organisation Beat, described it as a "very positive first step", and urged others to follow suit.
"[Tumblr] is a visual site and that is what is so concerning, when some of those images may be encouraging people to damage their health and do things that are very harmful," she told Newsbeat.
"These images don't cause eating disorders by themselves but people who have already got serious problems can make it harder for people to recover."
However, more than 1,700 people have signed an online petition urging Tumblr to stop removing the blogs.
Text posted alongside the petition expresses concern that Tumblr's new policy could penalise people for discussing their thoughts and feelings, thus damaging a support community.
It adds: "We, as the users of Tumblr, often post or reblog content such as this, but NOT for the purposes of encouraging others, or ourselves, to engage in damaging behaviour, or for the purpose of triggering our own or others' mental disorders.
"We simply post this content because it is an accurate representation of our own thoughts and feelings that we would not otherwise be able to express: to us it is a form of therapy."
In a comment posted below the petition, someone called Jenn G posted: "I treat my blog like it is my diary. When I'm feeling self-destructive, I often use it to distract me or to make me feel like I'm not alone.
"I have friends that I've met on Tumblr that I talk to when I'm feeling triggered to cut or starve and they help me eat and stay clean. Not all of us are bad."
Other social media sites Facebook, Twitter and YouTube already impose restrictions on the promotion of suicide, self-harm or eating disorders, with users able to report pages and have them removed.
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