Is a mirror's surface transparent, translucent, or opaque? How do you know?

Opaque

We need to define first what kind of mirror we are talking about here. Is it a common household one-way mirror or is it a two-way one? If it is only a one way mirror, then technically it is opaque (or has an opaque surface)

Technically, an opaque surface is one that never lets any shred of light pass through it. The light is either absorbed OR reflected. The point is, no light gets through. If you are using a one-way mirror (the one we use in our bedrooms and kitchen sinks), the reflective coating of the mirror merely bounces off the light shone in it. That's why we see an image, a "reflection". The light never gets through, only bounced back.

However if you are referring to a 2 way mirror, then it's a different story. On one side of the mirror, you see nothing but your reflection. However on the other side of it, it is like looking through a clear glass. Look for some images of a 2 way mirror in the internet if you want to know what it looks like. So, a 2 way mirror is technically both opaque, and transparent.