The difficulty is that, compiled with MinGW, GTKmm will necessarily use the libstdc++ library ; yet libstdc++'s ABI changed heavily between each recent versions of the compiler. That is to say, a binary library (.dll and .dll.a) compiled with version 4.5 will not be usable with 4.6, 4.7, and so on.
Hence my work-of-the-day, a clean developement environment for GTKmm 3 :
PS1 : do not install the environment in a path containing spaces ("C:\Program Files" e.g.). You have been warned !
PS2 : to test the library, download this sample and compile it by typing compile_gtkmm3 gtkmm3test.cpp.