I haven't seen the movie as graphic violence isn't really my cup of tea, but its easy to make a D&D game as bloody and violent as you want.
The main thing is adding graphic descriptions of what happens when creatures die. Entrials can spill out all over the floor. Blood squirts like a fountain. The creatures brains splatter against the wall. Limbs going flying in different directions and hit the ground with a wet *shlump*ing sound. Whatever. Personally, I get tired of this sort of thing in a hurry. Not only do I not get off on it, but even the most imaginative sort of person is eventually going to run out of descriptive, poetic, and evocative ways for a creature to be dismembered. After a while, who cares?
You could also add mechanics to support you goal. For example, you could rule that anytime a creature or character falls below 0 hit points, a secondary table is consulted to see what sort of dismemberment has taken place (hand removed at wrist, eye gouged out, skull split open, leg removed at knee, genitals removes, disemboweled, whatever). If you really wanted to get into it, you could have a whole bunch of tables depending on the form of the attack, and maybe another table for 'instant killing' blows that take the character below -10 hit points. But, while this has the 'positive' effect of explain how a person gets maimed under the rules, its probably not going to be all that fun for most groups because it makes the game much more dangerous at low levels of play (before spells become available to repair lost limbs and such).
You could even take this further and have every critical hit have a chance of an additional effect on the dismemberment table. This is 'gritty' and maybe even 'realistic' (and a throw back to an earlier style of RPG), but I'm not sure how well most groups would appreciate it.