I assume you are trying to duplicate the concrete scalloped edging ( sort of) that you can buy at Kmart. ANyway some type of edging for around a tree. Jumping ahead and assuming that you do create this edging --and it looks nice, the question will be ----- can you trim the grass around it. It you use a weed eater, I would think the sting would cut into the tufa ( since it is only a thin coat over the sytrofoam).
If you instead make solid hypetufa rocks ( about 4" x 6" ) kinda like those kobble stones sold along with pavers, you may have stronger object, than can withstand the trimmer or the lawn mower.

How about using the blue Styrofoam SM as a form for a kind of triangular rock with the cut-off point facing the tree? Carve a hole in the foam in the shape that you'd like. Doubling the width of the 2" foam would give you a rock depth of 4". I also think that a skim coat of hypertufa on a base of styrofoam, even with pebbles inbedded, won't be sturdy enough. I like 2" at least - 4 may be on the thick side.

Mercedes