For the third time in two days, I've just seen it spelt starting mini-, as in mini-skirt.
Two completely different roots, according to my office's Collins Pocket Dictionary of the English Language:
miniature - from Medieval Latin miniare, meaning "to paint red", itself deriving from minium, meaning "red lead" (red lead paint, you see).
minuscule - from Latin minuscula meaning, quite simply, "very small".
So there you go. No further excuses, now. ;o)