First, what reflects the light, whether it is UV, visible or IR wavelength, is the metal coating on the mirror. The reflectivity of various metals is indicated here: Page on www.layertec. read more
However, if the aluminum is on the Back Side of a piece of glass, the glass will absorb most of the UV light and therefore, No, a back-face mirror will not reflect much of the UV light. Unless the glass is special glass that has a a high transmissivity for UV. read more
If the mirror is made of glass, it won't reflect the all the UV light. This is a problem with making ICs, since the low wavelength lasers needed for modern ICs can't be reflected with a plain glass mirror. read more