Two part, five minute epoxy. Do everything you can to remove the old mirror, so the new mirror seats in the slot in the shaft, if there is one. Don't use CA(superglue), don't use silicone. CA fumes react with organics on the mirror and decrease the reflectivity.
You'll need to make a small jig to hold the mirror straight, centered, and flat. The epoxy surface tension tends to shift the mirror when curing. I've done it without a jig, but it is best if the galvo body is horizontal and you have a small block to hold the mirror level.
A bit off center is allowed, but two much side to side error causes a differential inertia that can show up in graphics. The mark one Eyeball is an OK centering tool, but a ruler or caliper, is a better idea.
The usual technique is to quickly heat the shaft with a soldering iron to loosen the remaining "old" mirror. One needs to do this carefully to avoid boiling or decomposing the oil in the bearings.
Steve