Post an アニメ with torture または very sad scenes that are very hard to look at...(I give props)

I'm gonna have to go with the obvious and say Higurashi: When They Cry (AKA Higurashi no Naku Koro ni). It's tragic and has some really tough scenes during Shion's arc. The deaths aren't softened at all, and despite it being a bit confusing at first, I'd say the story is pretty awesome. It has what your looking for without lacking plot and good characters.

I guess Danganronpa...

Tokyo Ghoul has some really sad scenes and torturous ones too

Elfen Lied has some really sad and bloody scenes. It's a great anime!

Corpse Party:Tortured Souls !!!!

Berserk

Shiki

I would recommend Bokurano. It's not much bloody, doesn't have any torture scenes, but almost from the beginning it could make あなた feel somewhat depressed. The main idea of this アニメ and the characters' fates are really sad. It also deals with a lot of death.

I'd say エンジェル Beats. It does give of comedy, however every character's story is told with a bit of shocking depth that I found extremely sad.

Arietty, especially the ending! There is no torture but one of the characters might die (you don't find out, but he has a ハート, 心 illness) and it is very tear jerking when Arietty gives him her hair clip (I know it sounds weird but it makes sense when あなた watch it.

Also The Girl Who Leapt Through Time, there are many deaths (but the girl time travels to before it happened to prevent it happening again) and the ending is sad.

Akame Ga Kill!
Chelsea's death, her fingers were shot off, her arm was severed, she got another bullet through the back, then her head was taken off and placed on a pole.
and that's not taking into account what happened to the rest of her body.....