When blue light encounters a mirror, it behaves in the same way as any other visible light. A mirror reflects light, regardless of its color or wavelength, including blue light.
If you are on the opposite side of a mirror, looking at a TV through the mirror, the blue light emitted by the TV will still be reflected by the mirror and reach your eyes. The mirror's reflective surface reflects the blue light rays incident upon it, preserving the color and characteristics of the light.
So, yes, if you are looking at a TV through a mirror, the blue light from the TV will still be projected and visible to you. The mirror reflects the light, allowing you to see the image of the TV as it would appear without the mirror.