As the thread slowed down a bit, I think I will try and chime in back into the discussion again. And as the problem of turning the other cheek is being discussed right now, I will try to concentrate on that, but there is one important thing that is a little more universal, regarding the literal/metaphorical reading of the Bible. Some people wonder why Bible is so open to interpretation, i.e. why God didn't give us more precise answers to all the questions; as far as I know, the answer is: so the Bible will remain universal over the time. Times change, and with times change people, but the Bible does not (aside from a single event, the coming of Christ, but that was sequel that was anticipated from the beginning), so it must be open enough to be understandable to people of all times, and relevant to people of all times. That's why 'thou shall not kill/murder' doesn't state 'you shall not take life of another person, unless as a punishment for capital crime, if such punishment is applicable in your country, which should only be when there is no possibility of achieving such ends with less drastic policy, like permanent isolation of criminal [...]'. Those things (this is the part of the current view on capital punishment of Roman Catholics, BTW) we have to come to ourselves, using other parts of the Book.
That being said, in case of mugging, you are viewing the stuff a little too narrow. If you are the only person that has anything to do with your money, and you have a job, it is perhaps the best course of action to give to the demands and give up your wallet with all the money; you only lose some of your earthly possessions, and this are not really important for you. But if you (example 1) have no job, and this is all the money you have, and without it you are going to starve for God knows how long, and might die due to undernourishment, it is much worse idea; 'thou shall not kill' also means that you should care for your own life and well-being. Perhaps you can just give him a handful of money, or even convince him that without it you are going to die? Other possibility (example 2) is if you have, say, wife and four kids waiting for some food you went out to buy, and no savings. Not only you will be hurt by the lack of money, but also other people, people who you are supposed to take care of. In this case, I would say it is perfectly acceptable to use any means necessary to stop the mugging, and deliver the food to the kids. Yet another possibility is that you believe stopping the criminal and handing him to the powers of justice stands a good chance of him turning better; in this case, it is completely acceptable to stop him, even hurting him somewhat, and turning him to the authorities, because you are helping a sinner find a way to God, which is perhaps of the very best things you can do on Earth. Because of the more joy being brought to Heaven due to one sinner that repents than 99 just that... well, are still just.