Q. How can we show that Jesus did not mean that we should literally pluck out our eyes and cut off our hands but meant it figuratively when he said that?
This is an excellent question, because it helps demonstrate that we cannot just take statements in the Bible and follow them literally without considering their literary and cultural context. When we do consider the context of the statements you are asking about, we realize that Jesus was following the practice of rabbis in his day and using overstatement for emphasis. (This is the rhetorical device known as “hyperbole.”) So the historical context is that Jesus was teaching the way Jewish rabbis did, and the immediate literary context is that rabbis used overstatement or exaggeration as a teaching tool. The goal behind the use of that tool was to provoke further reflection.
Beyond this, the broader literary context of any individual statement in the Bible is the Bible as a whole. Every statement needs to be understood within that broader context, which is sometimes called the “whole counsel of God.”
So let us consider the statements you are asking about. In the Sermon on the Mount, speaking about temptations to sin, Jesus said, “If your right eye causes you to stumble, pluck it out and throw it away. It is better for you to lose one part of your body than for your whole body to be thrown into hell. And if your right hand causes you to stumble, cut it off and throw it away. It is better for you to lose one part of your body than for your whole body to go into hell.”
One thing we can say about this right away is that if it is taken literally, it goes against the emphasis that we find all through the Bible on human wholeness and well-being. It also goes against the further emphasis that temptations to sin arise from within a person, from their desires, and that it is those desires that really need to be addressed and transformed. So the “whole counsel of God” suggests that Jesus did not mean for us to take these statements literally.
Rather, they are designed to provoke reflection that will lead us to understand the true source of temptations. “If it is, in fact, your eye that is causing you to sin, then pluck it out, if you really want to be free from sin. But if you would not do that, then you are acknowledging that it is actually not your eye that is causing you to sin, it is your desires, so you need to deal with those.” The logic is the same with the hand.
We see Jesus using overstatement in other teachings as well. “It is easier for a camel to go through the eye of a needle than for someone who is rich to enter the kingdom of God.” Basically, it’s impossible for a camel to go through the eye of a needle. But Jesus is not saying it’s impossible for a rich person to enter the kingdom of God. He is illustrating how very difficult that is for people to do that if they make riches their priority. “Which of you, if your son asks for bread, will give him a stone?” No parent would give a stone to a child who asked for food. This is another extreme illustration that Jesus used to make a point, in this case that God wants to give good things to us, his children.
So the whole gospel record of Jesus’ life and teachings show that he was a rabbi who used overstatement. We have every reason to understand what he said about plucking out eyes and cutting off hands as overstatements designed to provoke reflection on the true source of temptation, particularly when we consider these statements in light of the “whole counsel of God” in the Bible.
Good Question 
I can’t read the Bible, because as above, statements like plucking one’s eye out, etc. If the Bible is meant to be read by believers, and doesn’t make sense as read, why bother?
I appreciate your frustration, but I would say that the Bible is a book that invites reflection on its own meaning. If statements in the Bible don’t make sense when we first encounter them, we are meant to pause and meditate and reflect on what they may actually mean. We need to try to understand statements in the context of the Bible as a whole and in their original literary and historical context. In one sense the Bible is easy enough for a child to understand. In another sense a thoughtful person could spend an entire lifetime plumbing the depths of its meaning and get to the end of life with much meaning still to discover. So I would encourage you not to give up on reading the Bible, even when individual statements are troubling, but to see how reflection on them in light of the whole can yield insights and understanding.