Here is the passage in question:
Matthew 5:28 But I say unto you, That whosoever looketh on a woman to lust after her hath committed adultery with her already in his heart. 29 And if thy right eye offend thee, pluck it out, and cast it from thee: for it is profitable for thee that one of thy members should perish, and not that thy whole body should be cast into hell. 30 And if thy right hand offend thee, cut it off, and cast it from thee: for it is profitable for thee that one of thy members should perish, and not that thy whole body should be cast into hell.
First of all, as to the doctrinal context of this passage, I would agree men like C. I Scofield and Lewis Sperry Chafer in identifying the Sermon on the Mount as a Kingdom Age passage. Some have called it the "Constitution of the Kingdom" and I believe this is a good title describing its content. In this sermon, Jesus introduces a new level of responsibility for those who would be part of the coming kingdom. As seen in Matthew 5:28 and the other but-I-say-unto-you passages of this sermon, Christ takes the external commands of the Old Testament and extends them to the heart.
However, my calling this kingdom doctrine does not exclude those of us in the grace age from the spiritual demands of the Sermon. Three spiritual economies are extensively expounded upon in scripture: the law, the kingdom, and the age of grace. Because of its external commands and the New Testament teaching that we are no longer under the law, many have assumed that the law is much more demanding than grace. Those who make this assumption are wrong. As is obvious from the teaching of the Sermon on the Mount, kingdom doctrine is much more demanding than the law. What we often do not realize is that grace is much more demanding than either.
For example, consider the teaching against adultery. Under the law, a man was prohibited from committing adultery. In the kingdom, a man is committing adultery if he lusts after a woman. Under grace, we are to use spiritual warfare to bring "into captivity every thought to the obedience of Christ" (2 Corinthians 10:4-5). Certainly, the requirement that "every thought" is to be obedient to Christ is more demanding than the command to avoid lusting after a woman. However, there is also another difference in these three dispensations. The more demanding God is of us, the more of His enabling He provides. The Old Testament saints did not as a rule have the indwelling Spirit of God. We do.
All of this means that we can learn from the moral demands of both the law and the kingdom age. But God works with us through the indwelling Spirit. Romans 8:4 states, "That the righteousness of the law might be fulfilled in us, who walk not after the flesh, but after the Spirit." The law was based on the righteousness of God. But the fact that we are no longer under the law does not mean that we are not required to live righteously. On the contrary, we are to achieve the underlying righteousness on which the law was built by the power of the Spirit working in us. If, then, the law teaches us about the righteousness of God, then certainly the kingdom passages will do the same.
Now, let us consider Matthew 5:29-30 and the "advice" to pluck out the eye or cut off the hand. Jesus pretty much repeats this teaching in Matthew 18:7-10, only here the offense is the offending of little ones--not looking lustfully on a woman. It is difficult to see how the eye would be the offender in this case, but both the eye and the hand are mentioned as better removed than going to hell.
Is Jesus actually recommending that anyone cuts off a hand or plucks out an eye? I do not think so. First of all, He qualifies both statements with an "if" and a "better." That is, "if" your right eye or right hand would keep you from going to hell, then it would be "better" to lose them then to go to hell. Certainly, anyone who understands the judgment of hell would agree with this comparison. However, Jesus never states that maiming the body in any way would get anyone in heaven. He is using comparison to make a point: that losing important members of the body is not nearly as serious as going to hell.
Another evidence that he is just making this point is found in the nature of the maiming. The sin just mentioned is that of looking on a woman lustfully. Is it not just as likely for a man to lust after a woman with one eye as it is with two? For the maiming to really be effective, he would have to pluck out both eyes. But that is not the point. The point is that the pleasures of this life are not worth going to hell over. This is a truth that certainly crosses the dispensations.