Hermeneutics: Scripture has two "senses": a literal (historical) and a spiritual (the message God is trying to get across to us). (See here for further explanation of this.) The Bible is completely true in both senses.
Literal: Jesus literally said that "if your eye causes you to sin, tear it out and throw it away." This statement should be taken as an historical fact. (It is not just some life lesson that Matthew made up to teach us something.)
Now, what was God trying to get across to us by Jesus saying this? That's where we jump from "literal" to "spiritual".
Spiritual: If anything in your life causes you to sin, be ruthless about tearing it out of your life and casting it away from you. This is serious business. It is much better to lose things you value in this life than to go to Hell for eternity!
But does this apply to ripping your eyes out? Yes! It applies to everything! If your eye causes you to sin, rip it out!
Application: With that said, your actual, physical eye does not cause you to sin. It's just blood vessels and goo. What causes you to sin is your lust, etc. And it is that lust that needs to be ruthlessly ripped out of your life.
This is easy to see if you consider what would happen if you actually ripped your eyes out. Do you think you would suddenly stop lusting? Man... if it were that simple, I'd happily go blind!
Conclusion: The Bible is literally true, but the purpose behind it all is to convey spiritual truth. The truth in this case is that we must rid our lives of those things which cause us to stumble - even if it's something as precious to us as our own eyes. Unfortunately, it is not that simple; your eye is not the cause of your stumbling.