There are several parallel hand removal scenes in the Star Wars saga, but Luke cutting off Darth Vader's hand in "Return of the Jedi" is the most obvious.
Darth Vader lost his left arm and both legs when Obi-Wan Kenobi defeated him on Mustafar. After turning to the dark side of the Force, Skywalker severed Mace Windu's right hand to save Darth Sidious when Windu tried to kill the latter.
Mechno-arms were cybernetic replacements to hands and arms lost in a variety of situations, but more often than not by lightsaber blades. After Count Dooku severed the right arm of Anakin Skywalker in the opening battle of the Clone War, a mechno-arm was grafted to what was left.
Luke cuts off one of Vader/Anakin's artificial hands in Return of the Jedi.
In Star Wars Episode VI: Return of the Jedi, Luke Skywalker noticed after cutting Vader's hand off that Vader who used to be Anakin Skywalker was largely a machine. Vader was a puppet to Emperor Palpatine for years, and since Luke did cut off his cybernetic hand; he saw this as a true warning of the dark side.
In Return of the Jedi, Darth Vader's body — armor, mask, and all — was burned in a funeral pyre by Luke Skywalker, Luke's final act of honoring his father.
“You were right about me. Tell your sister... you were right.” Those were the last words Anakin Skywalker, aka Darth Vader, ever said while he was alive.
Luke Skywalker
He is Force-sensitive and skilled with a lightsaber. In Return of the Jedi, a dying Yoda confirms to Luke, that Darth Vader (formerly Anakin Skywalker) is actually his father, despite Luke's belief that Vader's claim to fatherhood in The Empire Strikes Back was a ruse to pull Luke to the dark side.
The duel progressed through the city's processing vane and onto a maintenance catwalk where Vader disarmed Skywalker by slicing off his weapon hand. He then tempted the young Jedi apprentice to join him and embrace the dark side. When Luke refused, Vader revealed that he was the boy's own father, Anakin Skywalker.
George Lucas didn't plan on making Darth Vader the secret father of Luke Skywalker. As much as fans have been told that Lucas had a massive plan for the Star Wars saga prior to 1977, the sources closest to that process say the opposite.
Darth Sidious
In the end, Vader managed to fulfill the prophecy tied to him. As for Darth Sidious, he's by far the most dangerous enemy Vader has had. Becoming emperor of the galaxy and crushing most of the Jedi was proof enough.
In Star Wars Canon, only Luke Skywalker can be acknowledged as the one who truly defeated Darth Vader.
In the original trilogy, Palpatine is depicted as the Emperor of the Galactic Empire and the master of Darth Vader (Anakin Skywalker).
In the duel, Anakin lost both of his legs, his one remaining organic arm, and suffered (possibly up to) fourth-degree burns across what was left of his body that were severe enough to damage his internal organs.
As a young Jedi Knight, Anakin lost a hand in a battle with Count Dooku, which received a robotic replacement. He later returned the favor by removing both of Dooku's hands. Eventually, he lost both his legs and his remaining arm in the climactic duel on Mustafar between both he and Obi-Wan.
If he were to take his mask off, the Sith Lord would soon suffocate. So it's the most crucial part of his armor. He can only breathe without the need for his mask when he is in one of his meditation chambers seen in The Empire Strikes Back.
Vader was conflicted, but still brought Luke before the Dark Lord. The Emperor taunted and tempted Luke, leading to a final duel between Vader and his son. Giving in to his hate, Luke overpowered Vader, cutting off his hand and was poised to deliver the killing blow.
He does. Right at the end. With Luke crying over him and Vader sensing his anguish and pain he had inflicted on all those who had cared for him.
Darth Vader is the product of Anakin's trauma and poor life decisions, which makes him the wiser, stronger half of the one-man duo when he returns in Episodes 4-6.
During the iconic opening moments of Star Wars: A New Hope, Darth Vader has a tense confrontation with Princess Leia, an adversary who, unknown to him, is actually his daughter. Despite participating in Leia's interrogation, the Sith Lord doesn't uncover his familial connection with the rebellious royal.
Once more, Darth Vader learns the name in the opening scene of an issue (in this case Vader's Quest #1) while torturing a Rebel, though in this case, he only learns Luke's surname of Skywalker, making the Sith Lord's discovery in the classic Marvel series Luke's first name.
Anakin Skywalker carried this blue-bladed Jedi weapon throughout the Clone Wars. After dueling his former apprentice on Mustafar, Obi-Wan Kenobi took Anakin's lightsaber and kept it on Tatooine for nearly two decades. He gave it to Luke Skywalker, who lost it when Darth Vader struck off his son's hand in Cloud City.
“You don't know the power of the dark side! I must obey my master.” Darth Vader's internal struggle between the light side and the dark is truly shown in this quote.
When Luke enters the cave he sees Darth Vader. He is confronted by his fate, and when Luke strikes down Vader to reveal his own face in the mask. It demonstrates that Luke's self-confidence in his skills to beat Darth Vader will ultimately result in his death. The idea is simple.
So he was confronted by Vader, who also embodied his fear. He lashed out in anger against the fear, which was another step on the path to the Dark Side. So Luke's face in Vader's helmet symbolizes his succumbing to fear, and from there, to the Dark Side.