The issue is: SFML 2.1 and older were built wrong for the TDM compilers - yes this is yet another TDM is stupid story.
TDM compilers link the runtime libraries (i.e. libgcc & libstdc++) statically by default, as opposed to any other GCC-like compiler. Previously SFML didn't account for that and thus even if you left
SFML_USE_STATIC_STD_LIBS unchecked the runtime libraries were linked statically. This unintended behavior was fixed and the result is, that you'll need the runtime libraries if you leave the option unchecked. The SDK packages on the download page, have been built without
SFML_USE_STATIC_STD_LIBS.
If you want them to be linked statically, you'll have to build SFML statically and check that box.
If you don't want to link statically, you need to add
-shared-libstdc++ and
-shared-libgcc to your linker flags and copy over the DLLs from your compiler binary directory.