As the Mac mini has no battery, would it fail or just suspend if the power is cut? I was interested in buying a Mac mini for work (I love Linux but it requires too much maintenance).

However, it turns out that it has no battery at all (different to a MacBook Pro/Air etc).  

I have never owned a Mac and I would like to know what happens if electrical power is missing for a few seconds? (It happens.)

Does it have kind of "snapshot" function or would it result in losing everything I was doing (if not saved)?
As with any computer which does not have a battery you will lose everything not saved to disk if you unplug the computer from the power  supply. If you use a Mini in an unstable environment, adding a UPS might reduce the risk of data loss.