Jesus did not mean for us to literally maim ourselves, but He exaggerated to drive home the point that we are to resist sin even to the point of shedding our own blood (Heb 12:4). Moreover, Jesus may have been revealing to us something about human nature: in some areas of each person's life, one must be careful not to overindulge but to abstain. This is the great insight of the Twelve Steps Programs.
For some, one drink is too many. Maybe you don't have a problem with drinking, but you can be in trouble if you have a TV, begin to gamble, eat one candy bar, drink one cup of coffee, go into a store with a credit card, access the Internet, etc. We will never be free if we don't come out of the denial that certain things in our lives must be completely cut off. The Lord could grace us to control our use of these things, but it seems that instead He has decided to call us to abstain in certain areas.
Know your calls to abstain, cut out what God wants out, and be free. It's better to abstain than to remain a slave. It's better to abstain than to lose your soul.