There are multiple acts of thievery, murder/manslaughter, accidental death, poking human eyes out, amputation, kidnapping, elder abuse, and child neglect.
The film is very dark and, at times, violent. It should be noted, though, that most of the violence is macabre and largely played for laughs.
Jack's mother, while not outright abusive, does tend to slap her child around during the prologue. Jack seems to be brain-addled, and we're slightly led to wonder if the mother's "abuse" is to blame.
After Cinderella accidentally ties her hair too tightly, one of her stepsisters slaps her, after which both stepsisters burst into hysterical laughter. This is not a very violent scene, it might upset some viewers as it is not done in a comedic way like most other violence.
Red Riding Hood is seemingly stalked and (later) eaten by The Wolf. Later, the Wolf is cut open with a knife (off-screen) and Red Riding Hood and her grandmother walk out, unscathed, but severely grossed out. Later in the film, emboldened by surviving her experience, Red becomes (for lack of a better word) trigger-happy, brandishing a knife and threatening to cut Jack open if he comes any closer. This is done for laughs and is not scary.
When the Prince is out looking for Cinderella via the slipper, he stops by Cinderella's house. There, the Evil Stepmother cuts off sections of the two stepsisters' feet so the shoe would fit. It is again played for comic effect, but you see the Stepmother making a strained cutting motion and the stepsisters crying out in agony. Later, when they are both passed off as the right girl, they are wincing walking in the slipper, and the slipper drips blood.
When Cinderella is discovered as the girl for the Prince, as they ride off together, a flock of birds swarm the evil stepsisters and blind them. They are later shown walking around with canes and sunglasses.
The Witch and Rapunzel have another heated shouting match. This is more real-feeling as it is not done through song.
It's also worth mentioning that the Witch's transformations (there are two, plus one mostly played-out offscreen) are very intense and they move her in violent ways.