Why did Darth Vader cut off Luke's hand?

I don't think it was really done intentionally. But then again, Vader was prepared to do anything to try and convince Luke to join him in the Dark Side.

This is very brief and basic.

This was a form of foreshadowing, a way to illustrate the similarity between Anakin/Vader and Luke. We see in Episode three how Anakin is consumed by rage and succumbs to the dark side, and in karmic fashion loses his limbs, symbolically consumed in fire. With the perception that he caused Padme's death, Vader (Anakin is now stripped away) gives up the last of his humanity as he screams in grief. In his battles with the older Vader, Luke is losing his grip on his own humanity and is giving in to his own anger. The positive influences in his life, Obiwan, Yoda, Leia, Han, C3PO and R2, even his Uncle Owen and Aunt Beru, all help to keep him anchored, something Anakin never had as he becomes Vader. This is illustrated in Episode V, when Luke is hanging from the antenna below Cloud City, he visibly gives up the rage and collapses into the arms of Lando and is rescued, both physically and spiritually, through the open hatch of the Millennium Falcon.