Violence isn't common. But when it does things do get somewhat violent. It is pretty surprising when it does happen since it is so infrequent. Renton and Holland get into fights multiple times in the first half of the series, none are particularly violent. Mech battles appear here and there, a part that could be a creepy factor for some is that the mechs can bleed when injured.
In one episode, Renton, while piloting a mech (LFO), goes into battle and relentlessly beats several of the other mechs leaving blood on the floor, and more disturbingly, we briefly see an arm in the pool of blood, causing Renton to feel bad about what he just did. In another episode, a woman sees her husband dead on the floor, she then kisses him on the floor but leaves a bomb, after the bomb explodes and the smoke clears we see nothing left except a blood splatter on the ground.
Another episode we see fish-like monster attacking a city, killing civilians and some blood is shown. At least twice, we see one of these monsters explode, this is slightly graphic, but avoids being too strong.