This does seem extreme that one should take this literally and actually cut off a hand, but would it be better to have two hands and end up in hell? That is the proposition that Jesus is presenting. He is balancing all you have in your life that is holding you back and preventing you from having a relationship with Him against the prospect of spending eternity in hell. The subject of hell is not brought up often enough in church today; it is an unpleasant subject and we mustn't upset the congregation. But Jesus is serious here.
Each year the world remembers the death and resurrection of Jesus because there is a hell! Jesus did not die as a martyr, but as a substitute in our place, on the cross to make a way of escape for each one who would receive Him. If there is no judgment of sin -- no hell to be afraid of -- there would have been no need for Christ to go to the cross. The reality of hell, with its eternal flames, was real to Jesus, and that is why He said if your hand is keeping you from receiving Him, it was better to cut it off than to go there!
But it is not the hand that keeps us from turning our lives over to Jesus. It's the wrong crowd of friends and the wrong places we go. It's alcohol and dope and lustful pleasures, or maybe a destructive self-image, or a past that we can't forgive and forget. They stand in the way.
However; all this can be changed and washed away in a minute by turning your life over to Jesus Christ, the risen Lord.