If you want to use tty emacs with mintty, you will probably need to use cygwin's emacs. The native win32 emacs wants to talk to a Windows console window, not to an actual tty -- the error message is misleading here.
Another alternative, if you want to stick with the native win32 emacs, is to use ConEmu, rather than mintty. It gives a compatible Windows console interface while also providing all the niceties of a normal terminal emulator like mintty.