Yes, but not only once. In "Revenge of the Sith," Obi-Wan defeated the duel against Vader by cutting off both of his legs and his left arm. And in "Return of the Jedi," Vader got his right hand cut off because Luke Skywalker was giving into anger and he was dueling Vader within his rage. When Vader was originally Anakin Skywalker in "Attack of the Clones," Anakin lost his right arm during a duel with Count Dooku on Geonosis.
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Yes. In Episode 2: Attack of the Clones, while in a lightsaber duel with Count Dooku, Anakin lost his right arm to Dooku's lightsaber and had to be replaced with a cybernetic prosthetic
No, Vader cut off his right hand.
Vader's right hand was another time cut off throughout his exchange blows at the meeting on Kessel when he was penetrating for Kenobi.
Vader cut off Luke's RIGHT hand.
Source: http://starwars.wikia.com/wiki/Star_Wars_Episode_V:_The_Empire_Strikes_Back#Duel_with_the_Dark_Lord
and luke cut of vader´s right arm
Yes, Darth Vader does cut off Luke's hand near the end of The Empire Strikes Back.
Darth Vader
The empourer was off guard and was nearly beat by mace window who was not as skilled a darth vader
Luke is resisting giving in to the Dark Side, so Darth Vader is fighting Luke with his light saber, and cuts off Luke's hand to show him his power, and to even further persuade him in joining him (Darth Vader) on the Dark Side. This act of cutting someone's hand off is called Cho Mai according to Jedi records. This is considered merciful by most Sith Lords who prefer killing their opponent.
no I'm Darth Vader, oh well fine I'm Jeff Vader and no you can't have my autograph f*** off.
If you mean when Vader's mask was taken off, the actor was Sebastian Shaw