I opened CMake MR 7804 to clarify the documentation.
You should be able to achieve your use case with:
$ env CXXFLAGS='-new -flags' cmake -U CMAKE_CXX_FLAGS ...
The -U CMAKE_CXX_FLAGS flag will undefine the cache entry so that it will be re-initialized using the new CXXFLAGS environment variable value in combination with the builtin defaults.