So why not cut them? Some trees permit the removal of certain roots; others will not. Trees vary by genus as well as individual. Cutting a root may kill a tree fairly quickly. For instance, you may chop a root to prevent further damage to your driveway and the next year be faced with the cost of a crane removal of the entire tree which then threatens to fall on your house. In that case, it may have been wiser to give the tree 10" of driveway. A certified arborist can tell you (without cost) whether your tree needs removal or can withstand loss of a root. In some cases, long term root growth can be influenced by the supply of water and nutrients. In all cases, the sooner the problem is addressed the better the results. Waiting to deal with a large root until it has lifted your garage four inches is not a prudent course of action. Look at your roots now, they're giving you clues on where they intend to grow.
If you're planning to live in your house for many years and you want to plant a good-sized tree, please call the office and we'll happy to recommend planting distances to minimize the likelihood of your tree ever causing structural damage. In the meantime, please don't cut roots.