The specification is mainly driven by optical and environmental constraints. The applicable technology is chosen according to these major issues.
For example, a wide set of materials can be used, in principle, for a space mirror (from polished Aluminium, to metal coated composites, honeycomb, etc.). But the choice must be justified with a dedicated trade-off (e.g. considering lifetime, optical and mechanical tolerances, temperature, stability in temperature and time, degradation of the optical properties, area and mass, etc. etc.)
Another parameter is the operational range of the mirror (shall it reflect visible light, UV or infra-red radiation?).
The thermal stresses are the main responsible for buckling in the short and medium term (for example, the thermal cycling day/night along one orbit, orbital manoeuvre, seasonal changes between summer and winter). In the long period other mechanical causes may intervene, such as creep or fatigue. These can be generated e.g. by the thermal stresses, when the optical structure is highly hyperstatic.
These effects are generally reduced by using a proper design, which is improperly defined "iso-static mount" (it is a hyperstatic mount, actually!), or even "kinematic mount". The principle is that, when a thermal stress is induced from environmental conditions, the consequent strain is absorbed by an elastic supporting system. Without entering in detail, this kind of mount should allow a easy deformation of the optical item (mirror, lens or whatever), with a limited buckling and a maintenance of the proper position within the optical path.
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Fatti non foste a viver come bruti / Ma per seguir virtute e canoscenza (Ye were not made to live like unto brutes / But for pursuit of virtue and of knowledge) (Dante Alighieri)
NASA had been toying with a design that used an inflatable ring and double-walled, compartmentalized reflective surface (sort of like a rolled up condom without the reservoir tip). By varying pressures in various compartments, they could change its characteristics. It was cheap (relative) and light and could be deployed anywhere in space, even orbiting other planets or asteroids. I lost track of their development path and don't know how far they got.
I don't imagine there are ISO standards or DIN norms for mirrors in space, outer or inner. Your big problems are the accelerations ('shock and vibration') on it's journey into orbit and differential expansion effects if its temperature in service is significantly different from where it was constructed, or particularly if it orbits in and out of line of sight of the sun (i.e. flies in and out of the shadow of a planet such as the Earth or it's moon). Can you be more specific about conditions it will experience?