The saying is very definitely American, hardly known elsewhere. The fact is, we’ve lost its second half, which makes everything clear.
The full expression is happy as a clam at high tide or happy as a clam at high water. Clam digging has to be done at low tide, when you stand a chance of finding them and extracting them. At high water, clams are comfortably covered in water and so able to feed, comparatively at ease and free of the risk that some hunter will rip them untimely from their sandy berths. I guess that’s a good enough definition of happy.
http://www.worldwidewords.org/qa/qa-hap1.htm