The violence is constant, but mostly mild and non-graphic.
A man is suddenly ambushed; struck in the head and knocked unconscious by a wild animal's hand, and dragged away by the creature.
A man is seen in a creature's cave, hanging upside down with a bit of blood on his face. The creature is very briefly seen eating the gory remains of another dead creature. The creature then comes over to the man to kill him, and the man visibly cuts off its arm with his lightsaber. In the Special and subsequent edition of the film, we very briefly see the creature crying out, and a bloody stump where it was injured.
A large animal used as a beast of burden keels over and dies due to freezing. Han Solo uses Luke's lightsaber to cut the animal open in order to put Luke inside to keep him from freezing to death. The animal's white fleshy muscle/fat is exposed, but there is no blood.
A closeup of a pale man's scarred visage with a nose clamp and breathing tube affixed may be found slightly creepy to some viewers. (The scars belong to the actor then-recovering from injuries sustained in an automobile collision.)
There is a large battle scene near the beginning of the film, where several uniformed combatants are killed onscreen, or are implied to have been killed. In the battle, there are three instances of a laser-firing, gigantic, robotic, elephant-like walking craft (an AT-AT "walker") being brought down and exploding into a fireball, killing its inhabitants.
A pilot's wingman is shot dead by a laser blast from inside their fighter craft. He slumps forward, dead. When the fighter is shot down and crashes, an AT-AT "walker" steps on the remains of the ship, including the dead wingman, while the pilot barley escapes before the ship is crushed.
The back of a man's horribly scarred head (enough to be bald) is briefly shown.
There are two instances whereby Darth Vader telekinetically chokes a man to death. There is no blood, but we see them moan and struggle to breath until they slump over and die. Intense.
"He will join us or die, master", a character vows.
An apparition of Darth Vader is decapitated by Luke Skywalker. We do not see any blood or wounds, but the lightsaber clearly cuts the head off and falls to the ground, where we visibly see the mask explode and Luke's face in it. Could be disturbing for some.
Upon seeing Darth Vader in the dining hall in Cloud City, a man draws his laser gun and shoots at him, but Vader telekinetically draws the laser bolts to his own hand, using the Force to block/deflect them, before telekinetically pulling the gun out of the man's hand.
A man is tortured offscreen, though the very first bits of the treatment (the man being placed face-first into a sparking electric device) are depicted. We hear audible screams from the outside of the closed doorway to the torture room.
A man is frozen in a block of a dull-colored metallic substance, and this block is pushed to the floor. The frontal part of the man's figure, especially man's face and hands, while appearing coated in the same substance as the block, can be seen protruding from it. Not violent but intense. Not gory but ugly/horrifying.
A man's hand is cut off by his opponent in an intense, prolonged lightsaber duel, in which both participants are generally battered and injured.
A number of Imperial stormtroopers are briefly shot with lasers. There is also a scene where Chewbacca knocks a few stormtroopers off a ledge.
Chewbacca chokes a man out of anger and frustration. We see the man strangling and trying to breath. He eventually releases the character.