I have a very large Norway spruce on the corner of my screened in porch. The porch has a cement floor that has had a crack across the middle of it. Over the past 15-20 years, the crack has raised the floor. Could this be because of the roots from the tree, and if it is, can I break up the floor and sever the roots without hurting or weakening the tree?
Yes, the roots are likely to be the cause of the cracks. Sadly you cannot remove the roots without hurting the tree.
If you have a spruce or pine that is within ten feet or so of your house it is prudent to remove it anyway. These trees can grow from 80' to 120' tall. If it falls on your house what is the potential for damage?
If you really want to keep a large tree close to your house call an arborist and have them do a health check. They will tell you how healthy the tree is and it's potential for a long life or otherwise.