It looks like hypertufa, which would be totally doable. You might want to have a look on the Facebook group that I'm on for some ideas (Warning: make sure you have a lot of time before going there - it's completely addictive) https://www.facebook.com/groups/89367815733/
Check out my blog at www.zazzyzee.blogspot.com I posted recently how to make stepping stones which would be the same technique as this clock. Hyperfufa would work too, but is a bit more involved than my technique.
I made something similar to this for my bathroom. I took a thick piece of cardboard and cut out the circle. Purchased sand from my local craft store and glued it on the cardboard. After it was dry I glued on shells. Using cardboard made it lighter for hanging up on the wall.
@Wendy M That's almost exactly what I was about to suggest. The only difference is that I was thinking thin plywood instead of cardboard.
plywood backing along with others suggestions
How about using a plate from the thrift store?
If this was made from "grout" it would be fairly heavy and awkward to hang. Perhaps a lightweight florist foam "core" that is layered with spray adhesive and beach sand.
@KMS Woodworks Great idea!
Just remember to leave access for battery replacement access in the back...otherwise...a short term clock!
Measure diameter of clock. Cut plywood about 4-5 inches larger in diameter, or recycle a table top.
Glue your shells down with silicone as @Karen @ The Decorated Nest suggested. I would think the hypertufa suggested by @Drought Smart Plants would be lighter weight than the sanded grout, but i am not sure if it would apply as easily as the grout.
I would get the lightest, thinnest plywood, cut a circle, apply plaster of paris-can get colored or add dry dye to get color--, place shells. and let dry. Be sure to cut a small hole so you can change battery and set time. Good Luck
Use a pizza pan , its shallow . Or a pan so that the cement can form around the clock edges....press in the shells when mortor is starting to set....let it cure. Oh, and I would spray the pan with cooking oil spray so it doesnt stick when you turn it over. Place a towel underneath to avoid breaking
You might be able to use paper mâché. The shells could be stuck into it because you would use glue to hold everything together. Probably a plastic bowl with a bottom about the size of the face of the clock would work. A shallow bowl. The clock face would face the outside of,the bottom of the bowl making the lip of the bowl hit the wall. Anything with some sort of flare. You may have to cut the bowl to make the depth fit the depth you want. Then you can have enough for you battery pack behind the face. The paper mâché would go on the bowl. It would be much lighter than cement. However I am not sure it would adhere properly. It's worth a try. And cheap. Elders glure and strips of paper, adding the shells. BTW, if you use plaste of Paris the coat should not be too thick. Just wanted to add that because it could crack.
Oh, just thought of using a pie tin. Cut out the bottom for your clock.