The game autosaves after you've beaten a boss. You can then load the checkpoint if you get a game over, or if you close the game and return to it later (note, however, that like all Twine games, TTTTTM uses browser storage to save your data, so it won't work in private browsing modes, and saves will be lost if you clear your browser storage!)
There is no way to save in the middle of a level, since this game was inspired by roguelikes.