Sooner or later, as a follower of Jesus, we have to reconcile scripture with scripture. We have to make passages like Matthew 5:29 square with Matthew 11:28. 
Matthew 5:29 If your right eye makes you stumble, tear it out and throw it from you; for it is better for you to lose one of the parts of your body, than for your whole body to be thrown into hell. 

Matthew 11:28 "Come to Me, all who are weary and heavy-laden, and I will give you rest.29 Take My yoke upon you and learn from Me, for I am gentle and humble in heart, and YOU WILL FIND REST FOR YOUR SOULS. 30 For My yoke is easy and My burden is light." 

The only explanation that makes these polar opposite passages work together for me is the concept of law and grace. 

Jesus was dealing with the Jewish leadership of His day who were justifying themselves by looking for loopholes in the law while at the same time burying under the law the very ones they were supposed to be teaching and helping. Jesus threw a stick of self–righteous dynamite right in the middle of those listening that day. They had to get real; playing the self-righteous game was over. 

The law can never justify anyone before God, it can only condemn. Only the grace of Jesus can save us from sin and give us a heart that wants to please God. In fact, Paul tells us the law can only cause our sin sick heart to rebel and get worse. 
Romans 7:5 For while we were in the flesh, the sinful passions, which were aroused by the Law, were at work in the members of our body to bear fruit for death. 

Before someone will turn to a savior they have to be convinced, by the law, that they are not acceptable to God based on their own behavior. Paul tells of the problem with the law–laden hearts of the Jews in his day and then gives the only grace solution. 
Romans 10: 2 For I testify about them that they have a zeal for God, but not in accordance with knowledge. 3 For not knowing about God‘s righteousness and seeking to establish their own, they did not subject themselves to the righteousness of God. 
4 For Christ is the end of the law for righteousness to everyone who believes. 

The law‘s job is to destroy self–righteousness as an option for relating to God so that the humble will turn to Jesus by grace as the only solution. In other words, once someone realizes the reality of Matthew 5:29 they are now ready for the grace of Matthew 11:28. 

Apart from this we are left reading law passages meant to terrorize self–righteousness and try to live by the guilt it induces as means of being right with God. Then we will read a grace passage and have temporary relief until we read another law passage. 

In order to square the whole Bible with itself and stop this spiritual schizophrenia, we have to be convinced that the law was meant to break us of self–righteousness and cause us, by grace, to fall at the feet of our savior as the only solution to our sin.