You might consider double headed nails or screws. I like screws, since nails can work out of the wall.
The link below would be a good style, and the last pic shows exactly how it would work with your mirror. This style also allows for adding D-rings, wire, or sawtooth hangers (even though the "artist" is wrong about the orientation of the sawtooth hanger as well as what a keyhole looks like). With your mirror, you can even use this style bare, although it would have a tendency to walk off the head and it would damage the paper backing.
I'm only suggesting these specific screws because they have a nice long shank between the heads. I'm sure the OP can find similar ones at a different retailers. Also, the variety of images in this listing are useful.
You can add D-rings without too much trouble and, with a pilot hole, without splitting the frame. Using screws will prevent damaging the frame and the mirror from shattering that a hammer and nails would almost guarantee. Adding a wire is almost a guarantee it won't be straight, and adding sawtooth hangers is definitely a guarantee of it being crooked, unless you add two of them. Usually sawtooth hangers are attached by nails, as I've already warned against.
You can also try hooks like these, but they might also allow the mirror to walk off the end and would damage the paper backing. These can also be used with D-rings and wires, but generally not with sawtooth hangers.