Bakemonogatari isn't a violent anime but there are some fight scenes and when they happen there is a lot of blood and has some gore. It's one of the tamest in the whole series.
In the first episode, there are a few quick montages of flashbacks showing a woman is seen with her limbs missing with a pool of blood, man holding a human's heart, cannibalism in a vampire fashion way, vomiting blood etc. This is very quick but noticeable.
A teenage girl threatening a teenage boy's mouth with a stapler and box-cutter knife. She presses the stapler (offscreen), he then pulls out with some blood seen. Nothing is graphic, but the idea of it may make people uncomfortable.
Kanbaru breaks Koyomi's hand wrist and kicks him in the face. She then began punching and beating him violently and kick him in the abdomen and in the face, sending him flying in the air with his intestines bursting out (she grabs by his intestines and spins him across the furniture). This scene is disturbing and bloody, although since the blood is shown in different colors, such as green, yellow, etc., the actions are a bit less violent than one would suspect.