This is linked to on every page of the site and explicitly on the Report page:  

 
It’s a <1day process that requires an account here (throw-away email and name, no email validation) and a site mod to contact the artist at the source to verify the account is legitimate. Given the source is wiped that’s now likely going to be impossible.
 
I suspect nobody actually reads the bold text in the big boxes.
 
 
“Why don’t people ask for permission before uploading?”  
Likely because at the end of the day it’s fanart of a copyrighted property owned by another company and people consider it made “for the fan community”; why else would post on a public site like Tumblr, where the artist receives no compensation different than here (a few fleeting “like” numbers)?. Probably also due to the large number of artists that express their delight on seeing their works shared here and elsewhere, with those opposed to it initially standing out and then be forgotten due to their self-initiated isolationism.
 
Given there’s no financial loss to the artist or the IP owner caused by the spread of fanart, and only potential gain in the case of commission artists gaining publicity, with pay-for works already deleted on-sight, people see sites like this (and there are plenty, this one is just the most popular) to be a boon to both the artists and fan community as a whole. It’s extremely doubtful that the fandom’s artistic side would have continued as strongly as it has without the boorus, imageboards, EqD Drawfriends and people just sharing things on forums or in chats.
 
But oh well.

@Background Pony #128A  
@Background Pony #128A  
dude I already told you how to get your art taken down. did you read the post at all? do you even care or are you just trying to raise a fuss?

@Background Pony #128A  
Calm down, the report button is still there.

@Reveal19  
Well I seem to be all the worse for it. I NEVER GAVE PERMISSION!!!! WHY IS THAT SO HARD FOR PEOPLE TO UNDERSTAND???  
I don’t care about “free exposure” or getting more people.  
At this point, I don’t think I even want to post art ever again. Obviously people consider me worthless, and my wishes regarding my work “strange” and pointless.

Wow, seems plenty of people think taking my work without permission and uploading on another site without asking me is a good thing. Here, let me just leave my house unlocked so you can just take whatever I own, after all, I should be soooo flattered that people want to share it with the world!  
Well, this makes quitting the pony fandom easier. Obviously artists aren’t respected.

@Background Pony #128A  
well it’s a good thing nobody “steals” art on derpibooru. Everything that’s uploaded is tagged with the original artist and has a link to the original source.
 
but if you really don’t want free exposure for your art, then feel free to put yourself on the DNP list  

@Background Pony #128A  
You have quite a strange position… Usually it’s a good thing to see someone’s art around, but not to you, why you can’t accept the fact that people love your art and share it for more people to see? I wouldn’t even found you if not derpibooru and did not follow your tumblr.

@Background Pony #A450  
I,the artist who never gave permission for my works to be reposted here, stopped using deviant art because third parties kept stealing my pony artwork from there. Apparently I just need to stop posting art all together.

Nice. You should consider uploading it on deviant art