Christ does not intend for us to take this instruction literally. Jesus does not want sinners to become physically handicapped. Because sin begins in the mind, the eye, the hand, or the foot cannot sin of and by themselves. Even without these body parts, a person can still sin.
Our Savior often employs figures of speech in His preaching. Here, He is simply using parts of the body to elucidate an important principle—that a Christian should not tolerate sin in his life. Once a sin becomes apparent, we should take immediate steps to eliminate it from our lives. By using the striking example of amputation, Christ also illustrates that the process of overcoming sin may be as painful as losing an arm, a leg, or an eye. Ultimately, it is far better to give up a sinful pleasure than to lose out on salvation (Hebrews 11:23-26). The apostle Paul expands Jesus' instruction in Colossians 3:1-17.