I can't help you too much with the planter itself, but before you begin building it, you will want to make sure that the soil, mulch, etc. that you place in the planter does not cover the trunk of the tree. The part of the trunk that has been above ground needs to remain above ground. The tree has to 'breathe', and burying a part of the trunk may cause the tree to rot and die. If this is a new tree, or if it has a planter around it already that you are replacing, then you shouldn't have any problems. I had a tree in my yard that had a pit dug out around it because it was in place before the house was built and the builders added soil to the rest of the property. The pit was caving in, and I had considered just filling it in, but was told by a tree expert that I would likely kill the tree had I done that. I ended up building a square retaining wall with landscaping 6x6 timbers, interlocked at the corners, and held in place with 1/2" rebar through the timbers into the ground at the corners. It measures 8'x8', and 3 timbers high. It looks nice and works great at preventing the soil from collapsing into the tree. In the Spring, I may build wooden planters for the four sides of the wall to add some color.
If the planter walls do not have to be too high, you should not need to use any concrete or mortar to hold the stones, but it depends on the types of stones. If the walls will be more than a foot or so high, you may want to consider concrete or mortar to prevent them from falling in/out.