My deck was built 30 years age around a Norway Maple. Now it has grown to the point that the roots are lifting parts of the deck. It is safe to cut or shave the roots that are lifting the deck?
Norway maple is one of the trees that is fairly shallow rooted, and frequently has roots above soil level. This happens regardless of the oxygen content in the soil, though it will produce surface roots much more quickly if the soil it grows in is very compacted.
It is not wise to shave or remove any larger roots - this may compromise the health of the tree. However, given it's uprooting your deck, you might want to consider removing that tree and planting a new tree. Otherwise, call an arborist, who should be able to give you good advice in respect of being able to remove any roots at all. Some information in this link here https://www.bowerandbranch.com/dealing-with-trees-with-surface-roots/#.W3xwrqDTUn4
In general, no because trees that have roots above ground need to have roots above ground. Usually, this is because the tree is having trouble finding the oxygen it needs from the soil.
That being said, Maple is one of a few species of trees that has a tendency to grow roots above ground despite living in oxygen enriched soil. So it might be possible for you to cut or shave the roots depending on the oxygen quality of your soil.
There are various methods for determining if your soil is oxygen rich or poor but the only method I have knowledge of is using a sensor. You can purchase them at your garden store or online. If you do end up going this route I would consult an arborist in your neighborhood first. Also, remember that if you reduce root volume you need to reduce canopy volume as well.
However, even if you soil is oxygen rich there are other problems that could crop up by cutting or weakening surface roots. Tree stability for instance. There are methods and steps that can be taken such as digging up the root and burying it further but to be honest it may just end up being more cost effective for you to build a new deck or update the existing one to cope with the tree's growing patterns.
Whew, shaving off the tops of those roots is just wrong! They are the trunks of the underground system of roots. A good carpenter could easily remake the deck to accommodate a growing tree. Simply jacking up the deck and extending posts or adding blocking will raise the deck easily. I'd like to see how the deck connects to the home. Is it level with the floor of your home or are you stepping up from the deck to get into the home?
If all you need to do is the area right around the base of your tree, the floor taken away can be made into raised benches and tables for potted flowers, food and beverages...that tree deserves to stay right where it is, it is part of your family by now, no shaving. To make it easier, make a square instead of a circle around your tree.
Spread crushed gravel around the base of the tree if there is too much mud. Even potted plants can be staged around the base. Please send a picture or two.